LMFDB - Embedded newform 23.3.d.a.14.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.3
Character	$\chi$	$=$	23.14
Dual form			23.3.d.a.5.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44626 - 0.424661i) q^{2} +(-0.590042 - 0.680945i) q^{3} +(-1.45368 + 0.934223i) q^{4} +(-1.77862 + 0.255727i) q^{5} +(-1.14252 - 0.734256i) q^{6} +(2.68734 + 1.22727i) q^{7} +(-5.65401 + 6.52507i) q^{8} +(1.16530 - 8.10482i) q^{9} +O(q^{10})$	\(q+(1.44626 - 0.424661i) q^{2} +(-0.590042 - 0.680945i) q^{3} +(-1.45368 + 0.934223i) q^{4} +(-1.77862 + 0.255727i) q^{5} +(-1.14252 - 0.734256i) q^{6} +(2.68734 + 1.22727i) q^{7} +(-5.65401 + 6.52507i) q^{8} +(1.16530 - 8.10482i) q^{9} +(-2.46375 + 1.12516i) q^{10} +(0.324790 - 1.10613i) q^{11} +(1.49389 + 0.438644i) q^{12} +(0.859718 + 1.88252i) q^{13} +(4.40777 + 0.633741i) q^{14} +(1.22359 + 1.06025i) q^{15} +(-2.53490 + 5.55065i) q^{16} +(12.8244 - 19.9551i) q^{17} +(-1.75647 - 12.2165i) q^{18} +(16.8785 + 26.2635i) q^{19} +(2.34663 - 2.03337i) q^{20} +(-0.749942 - 2.55407i) q^{21} -1.73768i q^{22} +(-22.9588 - 1.37682i) q^{23} +7.77931 q^{24} +(-20.8892 + 6.13363i) q^{25} +(2.04281 + 2.35753i) q^{26} +(-13.0284 + 8.37283i) q^{27} +(-5.05307 + 0.726522i) q^{28} +(-13.4745 - 8.65951i) q^{29} +(2.21988 + 1.01379i) q^{30} +(-25.8114 + 29.7879i) q^{31} +(3.60595 - 25.0799i) q^{32} +(-0.944855 + 0.431501i) q^{33} +(10.0732 - 34.3063i) q^{34} +(-5.09359 - 1.49561i) q^{35} +(5.87774 + 12.8705i) q^{36} +(59.3953 + 8.53975i) q^{37} +(35.5639 + 30.8163i) q^{38} +(0.774622 - 1.69619i) q^{39} +(8.38768 - 13.0515i) q^{40} +(-3.46071 - 24.0697i) q^{41} +(-2.16922 - 3.37538i) q^{42} +(6.13489 - 5.31592i) q^{43} +(0.561234 + 1.91139i) q^{44} +14.7134i q^{45} +(-33.7890 + 7.75844i) q^{46} +58.1561 q^{47} +(5.27538 - 1.54899i) q^{48} +(-26.3726 - 30.4356i) q^{49} +(-27.6066 + 17.7417i) q^{50} +(-21.1552 + 3.04166i) q^{51} +(-3.00845 - 1.93341i) q^{52} +(-36.3725 - 16.6108i) q^{53} +(-15.2868 + 17.6419i) q^{54} +(-0.294809 + 2.05044i) q^{55} +(-23.2022 + 10.5961i) q^{56} +(7.92496 - 26.9899i) q^{57} +(-23.1650 - 6.80184i) q^{58} +(19.0467 + 41.7064i) q^{59} +(-2.76922 - 0.398154i) q^{60} +(42.6597 + 36.9649i) q^{61} +(-24.6802 + 54.0422i) q^{62} +(13.0783 - 20.3503i) q^{63} +(-8.90898 - 61.9633i) q^{64} +(-2.01052 - 3.12843i) q^{65} +(-1.18327 + 1.02531i) q^{66} +(-22.4851 - 76.5774i) q^{67} +40.9891i q^{68} +(12.6091 + 16.4460i) q^{69} -8.00179 q^{70} +(-58.8521 + 17.2805i) q^{71} +(46.2959 + 53.4284i) q^{72} +(80.6553 - 51.8340i) q^{73} +(89.5276 - 12.8721i) q^{74} +(16.5022 + 10.6053i) q^{75} +(-49.0720 - 22.4104i) q^{76} +(2.23034 - 2.57395i) q^{77} +(0.400003 - 2.78208i) q^{78} +(19.8212 - 9.05205i) q^{79} +(3.08916 - 10.5207i) q^{80} +(-57.3197 - 16.8306i) q^{81} +(-15.2266 - 33.3415i) q^{82} +(59.7847 + 8.59575i) q^{83} +(3.47624 + 3.01218i) q^{84} +(-17.7066 + 38.7720i) q^{85} +(6.61520 - 10.2935i) q^{86} +(2.05385 + 14.2848i) q^{87} +(5.38123 + 8.37336i) q^{88} +(-52.9362 + 45.8694i) q^{89} +(6.24819 + 21.2794i) q^{90} +6.11407i q^{91} +(34.6609 - 19.4471i) q^{92} +35.5137 q^{93} +(84.1089 - 24.6966i) q^{94} +(-36.7367 - 42.3965i) q^{95} +(-19.2057 + 12.3428i) q^{96} +(-83.0916 + 11.9468i) q^{97} +(-51.0664 - 32.8184i) q^{98} +(-8.58653 - 3.92134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{21}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.44626	−	0.424661i	0.723131	−	0.212330i	0.100601	−	0.994927i	$-0.467923\pi$
$2$	1.44626	−	0.424661i	0.723131	−	0.212330i	0.622529	+	0.782596i	$0.286105\pi$
$3$	−0.590042	−	0.680945i	−0.196681	−	0.226982i	0.648839	−	0.760926i	$-0.275255\pi$
$3$	−0.590042	−	0.680945i	−0.196681	−	0.226982i	−0.845520	+	0.533944i	$0.820709\pi$
$4$	−1.45368	+	0.934223i	−0.363420	+	0.233556i
$5$	−1.77862	+	0.255727i	−0.355723	+	0.0511453i	−0.317860	−	0.948138i	$-0.602964\pi$
$5$	−1.77862	+	0.255727i	−0.355723	+	0.0511453i	−0.0378633	+	0.999283i	$0.512055\pi$
$6$	−1.14252	−	0.734256i	−0.190421	−	0.122376i
$7$	2.68734	+	1.22727i	0.383906	+	0.175324i	0.598013	−	0.801486i	$-0.295957\pi$
$7$	2.68734	+	1.22727i	0.383906	+	0.175324i	−0.214108	+	0.976810i	$0.568684\pi$
$8$	−5.65401	+	6.52507i	−0.706751	+	0.815634i
$9$	1.16530	−	8.10482i	0.129477	−	0.900536i
$10$	−2.46375	+	1.12516i	−0.246375	+	0.112516i
$11$	0.324790	−	1.10613i	0.0295264	−	0.100558i	−0.943412	−	0.331624i	$-0.892403\pi$
$11$	0.324790	−	1.10613i	0.0295264	−	0.100558i	0.972938	+	0.231067i	$0.0742216\pi$
$12$	1.49389	+	0.438644i	0.124490	+	0.0365537i
$13$	0.859718	+	1.88252i	0.0661322	+	0.144809i	0.939812	−	0.341692i	$-0.111000\pi$
$13$	0.859718	+	1.88252i	0.0661322	+	0.144809i	−0.873680	+	0.486502i	$0.838273\pi$
$14$	4.40777	+	0.633741i	0.314841	+	0.0452672i
$15$	1.22359	+	1.06025i	0.0815729	+	0.0706833i
$16$	−2.53490	+	5.55065i	−0.158431	+	0.346915i
$17$	12.8244	−	19.9551i	0.754374	−	1.17383i	−0.225506	−	0.974242i	$-0.572403\pi$
$17$	12.8244	−	19.9551i	0.754374	−	1.17383i	0.979880	−	0.199587i	$-0.0639602\pi$
$18$	−1.75647	−	12.2165i	−0.0975819	−	0.678697i
$19$	16.8785	+	26.2635i	0.888344	+	1.38229i	0.923782	+	0.382919i	$0.125081\pi$
$19$	16.8785	+	26.2635i	0.888344	+	1.38229i	−0.0354379	+	0.999372i	$0.511283\pi$
$20$	2.34663	−	2.03337i	0.117332	−	0.101668i
$21$	−0.749942	−	2.55407i	−0.0357115	−	0.121622i
$22$		−	1.73768i		−	0.0789856i
$23$	−22.9588	−	1.37682i	−0.998207	−	0.0598616i
$23$	−22.9588	−	1.37682i	−0.998207	−	0.0598616i
$24$	7.77931			0.324138
$25$	−20.8892	+	6.13363i	−0.835570	+	0.245345i
$26$	2.04281	+	2.35753i	0.0785696	+	0.0906741i
$27$	−13.0284	+	8.37283i	−0.482532	+	0.310105i
$28$	−5.05307	+	0.726522i	−0.180467	+	0.0259472i
$29$	−13.4745	−	8.65951i	−0.464637	−	0.298604i	0.287298	−	0.957841i	$-0.407243\pi$
$29$	−13.4745	−	8.65951i	−0.464637	−	0.298604i	−0.751935	+	0.659237i	$0.770879\pi$
$30$	2.21988	+	1.01379i	0.0739961	+	0.0337929i
$31$	−25.8114	+	29.7879i	−0.832625	+	0.960900i	−0.999686	−	0.0250461i	$-0.992027\pi$
$31$	−25.8114	+	29.7879i	−0.832625	+	0.960900i	0.167061	+	0.985947i	$0.446572\pi$
$32$	3.60595	−	25.0799i	0.112686	−	0.783748i
$33$	−0.944855	+	0.431501i	−0.0286320	+	0.0130758i
$34$	10.0732	−	34.3063i	0.296272	−	1.00901i
$35$	−5.09359	−	1.49561i	−0.145531	−	0.0427318i
$36$	5.87774	+	12.8705i	0.163271	+	0.357513i
$37$	59.3953	+	8.53975i	1.60528	+	0.230804i	0.885921	−	0.463836i	$-0.153527\pi$
$37$	59.3953	+	8.53975i	1.60528	+	0.230804i	0.719357	+	0.694640i	$0.244436\pi$
$38$	35.5639	+	30.8163i	0.935891	+	0.810954i
$39$	0.774622	−	1.69619i	0.0198621	−	0.0434919i
$40$	8.38768	−	13.0515i	0.209692	−	0.326287i
$41$	−3.46071	−	24.0697i	−0.0844075	−	0.587067i	−0.987500	−	0.157620i	$-0.949618\pi$
$41$	−3.46071	−	24.0697i	−0.0844075	−	0.587067i	0.903092	−	0.429447i	$-0.141291\pi$
$42$	−2.16922	−	3.37538i	−0.0516482	−	0.0803662i
$43$	6.13489	−	5.31592i	0.142672	−	0.123626i	−0.580601	−	0.814188i	$-0.697182\pi$
$43$	6.13489	−	5.31592i	0.142672	−	0.123626i	0.723273	+	0.690562i	$0.242637\pi$
$44$	0.561234	+	1.91139i	0.0127553	+	0.0434406i
$45$			14.7134i			0.326964i
$46$	−33.7890	+	7.75844i	−0.734544	+	0.168662i
$47$	58.1561			1.23736			0.618682	−	0.785642i	$-0.287667\pi$
$47$	58.1561			1.23736			0.618682	+	0.785642i	$0.287667\pi$
$48$	5.27538	−	1.54899i	0.109904	−	0.0322706i
$49$	−26.3726	−	30.4356i	−0.538216	−	0.621134i
$50$	−27.6066	+	17.7417i	−0.552132	+	0.354834i
$51$	−21.1552	+	3.04166i	−0.414808	+	0.0596404i
$52$	−3.00845	−	1.93341i	−0.0578548	−	0.0371810i
$53$	−36.3725	−	16.6108i	−0.686275	−	0.313411i	0.0415873	−	0.999135i	$-0.486759\pi$
$53$	−36.3725	−	16.6108i	−0.686275	−	0.313411i	−0.727862	+	0.685724i	$0.759486\pi$
$54$	−15.2868	+	17.6419i	−0.283089	+	0.326703i
$55$	−0.294809	+	2.05044i	−0.00536017	+	0.0372808i
$56$	−23.2022	+	10.5961i	−0.414326	+	0.189216i
$57$	7.92496	−	26.9899i	0.139034	−	0.473507i
$58$	−23.1650	−	6.80184i	−0.399396	−	0.117273i
$59$	19.0467	+	41.7064i	0.322825	+	0.706887i	0.999570	−	0.0293300i	$-0.00933738\pi$
$59$	19.0467	+	41.7064i	0.322825	+	0.706887i	−0.676745	+	0.736217i	$0.736610\pi$
$60$	−2.76922	−	0.398154i	−0.0461537	−	0.00663590i
$61$	42.6597	+	36.9649i	0.699340	+	0.605981i	0.930221	−	0.367001i	$-0.119615\pi$
$61$	42.6597	+	36.9649i	0.699340	+	0.605981i	−0.230881	+	0.972982i	$0.574161\pi$
$62$	−24.6802	+	54.0422i	−0.398068	+	0.871648i
$63$	13.0783	−	20.3503i	0.207593	−	0.323020i
$64$	−8.90898	−	61.9633i	−0.139203	−	0.968177i
$65$	−2.01052	−	3.12843i	−0.0309311	−	0.0481297i
$66$	−1.18327	+	1.02531i	−0.0179283	+	0.0155349i
$67$	−22.4851	−	76.5774i	−0.335599	−	1.14295i	−0.938543	−	0.345162i	$-0.887824\pi$
$67$	−22.4851	−	76.5774i	−0.335599	−	1.14295i	0.602944	−	0.797784i	$-0.293994\pi$
$68$			40.9891i			0.602781i
$69$	12.6091	+	16.4460i	0.182740	+	0.238348i
$70$	−8.00179			−0.114311
$71$	−58.8521	+	17.2805i	−0.828903	+	0.243388i	−0.668546	−	0.743671i	$-0.733083\pi$
$71$	−58.8521	+	17.2805i	−0.828903	+	0.243388i	−0.160358	+	0.987059i	$0.551265\pi$
$72$	46.2959	+	53.4284i	0.642999	+	0.742061i
$73$	80.6553	−	51.8340i	1.10487	−	0.710055i	0.144698	−	0.989476i	$-0.453779\pi$
$73$	80.6553	−	51.8340i	1.10487	−	0.710055i	0.960169	+	0.279421i	$0.0901425\pi$
$74$	89.5276	−	12.8721i	1.20983	−	0.173948i
$75$	16.5022	+	10.6053i	0.220029	+	0.141404i
$76$	−49.0720	−	22.4104i	−0.645684	−	0.294874i
$77$	2.23034	−	2.57395i	0.0289655	−	0.0334279i
$78$	0.400003	−	2.78208i	0.00512824	−	0.0356677i
$79$	19.8212	−	9.05205i	0.250902	−	0.114583i	−0.285995	−	0.958231i	$-0.592324\pi$
$79$	19.8212	−	9.05205i	0.250902	−	0.114583i	0.536896	+	0.843648i	$0.319597\pi$
$80$	3.08916	−	10.5207i	0.0386145	−	0.131509i
$81$	−57.3197	−	16.8306i	−0.707650	−	0.207785i
$82$	−15.2266	−	33.3415i	−0.185690	−	0.406604i
$83$	59.7847	+	8.59575i	0.720298	+	0.103563i	0.492709	−	0.870194i	$-0.336007\pi$
$83$	59.7847	+	8.59575i	0.720298	+	0.103563i	0.227589	+	0.973757i	$0.426916\pi$
$84$	3.47624	+	3.01218i	0.0413838	+	0.0358593i
$85$	−17.7066	+	38.7720i	−0.208313	+	0.456141i
$86$	6.61520	−	10.2935i	0.0769209	−	0.119691i
$87$	2.05385	+	14.2848i	0.0236075	+	0.164194i
$88$	5.38123	+	8.37336i	0.0611504	+	0.0951518i
$89$	−52.9362	+	45.8694i	−0.594788	+	0.515387i	−0.899421	−	0.437083i	$-0.856012\pi$
$89$	−52.9362	+	45.8694i	−0.594788	+	0.515387i	0.304633	+	0.952470i	$0.401466\pi$
$90$	6.24819	+	21.2794i	0.0694243	+	0.236438i
$91$			6.11407i			0.0671876i
$92$	34.6609	−	19.4471i	0.376749	−	0.211382i
$93$	35.5137			0.381868
$94$	84.1089	−	24.6966i	0.894776	−	0.262730i
$95$	−36.7367	−	42.3965i	−0.386703	−	0.446278i
$96$	−19.2057	+	12.3428i	−0.200060	+	0.128570i
$97$	−83.0916	+	11.9468i	−0.856615	+	0.123163i	−0.556609	−	0.830775i	$-0.687898\pi$
$97$	−83.0916	+	11.9468i	−0.856615	+	0.123163i	−0.300006	+	0.953937i	$0.596989\pi$
$98$	−51.0664	−	32.8184i	−0.521086	−	0.334882i
$99$	−8.58653	−	3.92134i	−0.0867327	−	0.0396095i
$100$	24.6361	−	28.4315i	0.246361	−	0.284315i
$101$	−14.8060	+	102.978i	−0.146594	+	1.01958i	0.775148	+	0.631780i	$0.217675\pi$
$101$	−14.8060	+	102.978i	−0.146594	+	1.01958i	−0.921742	+	0.387804i	$0.873234\pi$
$102$	−29.3043	+	13.3828i	−0.287297	+	0.131204i
$103$	−3.10249	+	10.5661i	−0.0301213	+	0.102584i	−0.973182	−	0.230038i	$-0.926115\pi$
$103$	−3.10249	+	10.5661i	−0.0301213	+	0.102584i	0.943060	+	0.332622i	$0.107933\pi$
$104$	−17.1444	−	5.03406i	−0.164850	−	0.0484044i
$105$	1.98700	+	4.35093i	0.0189238	+	0.0414374i
$106$	−59.6582	−	8.57755i	−0.562813	−	0.0809203i
$107$	−53.5096	−	46.3663i	−0.500090	−	0.433330i	0.367935	−	0.929852i	$-0.380065\pi$
$107$	−53.5096	−	46.3663i	−0.500090	−	0.433330i	−0.868024	+	0.496521i	$0.834610\pi$
$108$	11.1170	−	24.3428i	0.102935	−	0.225396i
$109$	−81.2899	+	126.490i	−0.745779	+	1.16045i	0.236244	+	0.971694i	$0.424084\pi$
$109$	−81.2899	+	126.490i	−0.745779	+	1.16045i	−0.982023	+	0.188761i	$0.939553\pi$
$110$	0.444372	+	3.09067i	0.00403974	+	0.0280970i
$111$	−29.2306	−	45.4837i	−0.263339	−	0.409763i
$112$	−13.6243	+	11.8055i	−0.121645	+	0.105406i
$113$	−14.8657	−	50.6281i	−0.131555	−	0.448036i	0.867198	−	0.497964i	$-0.165919\pi$
$113$	−14.8657	−	50.6281i	−0.131555	−	0.448036i	−0.998753	+	0.0499281i	$0.984101\pi$
$114$		−	42.3999i		−	0.371929i
$115$	41.1869	−	3.42233i	0.358147	−	0.0297594i
$116$	27.6775			0.238599
$117$	16.2593	−	4.77417i	0.138969	−	0.0408048i
$118$	45.2575	+	52.2299i	0.383538	+	0.442626i
$119$	58.9536	−	37.8872i	0.495409	−	0.318380i
$120$	−13.8364	+	1.98938i	−0.115303	+	0.0165781i
$121$	100.674	+	64.6990i	0.832014	+	0.534703i
$122$	77.3946	+	35.3449i	0.634382	+	0.289713i
$123$	−14.3482	+	16.5587i	−0.116652	+	0.134624i
$124$	9.69290	−	67.4156i	0.0781686	−	0.543674i
$125$	76.4485	−	34.9129i	0.611588	−	0.279303i
$126$	10.2727	−	34.9857i	0.0815295	−	0.277664i
$127$	112.648	+	33.0763i	0.886989	+	0.260443i	0.693325	−	0.720625i	$-0.256145\pi$
$127$	112.648	+	33.0763i	0.886989	+	0.260443i	0.193663	+	0.981068i	$0.437963\pi$
$128$	2.90478	+	6.36058i	0.0226936	+	0.0496920i
$129$	−7.23969	−	1.04091i	−0.0561216	−	0.00806907i
$130$	−4.23626	−	3.67074i	−0.0325866	−	0.0282364i
$131$	65.2272	−	142.828i	0.497918	−	1.09029i	−0.479223	−	0.877693i	$-0.659081\pi$
$131$	65.2272	−	142.828i	0.497918	−	1.09029i	0.977141	−	0.212594i	$-0.0681913\pi$
$132$	0.970398	−	1.50997i	0.00735150	−	0.0114392i
$133$	13.1260	+	91.2935i	0.0986919	+	0.686417i
$134$	−65.0388	−	101.202i	−0.485364	−	0.755241i
$135$	21.0313	−	18.2238i	0.155788	−	0.134991i
$136$	57.6994	+	196.506i	0.424260	+	1.44490i
$137$		−	82.4856i		−	0.602084i	−0.953611	−	0.301042i	$-0.902665\pi$
$137$		−	82.4856i		−	0.602084i	0.953611	−	0.301042i	$-0.0973345\pi$
$138$	25.2200	+	18.4307i	0.182754	+	0.133555i
$139$	−208.882			−1.50274			−0.751372	−	0.659878i	$-0.770608\pi$
$139$	−208.882			−1.50274			−0.751372	+	0.659878i	$0.770608\pi$
$140$	8.80168	−	2.58441i	0.0628692	−	0.0184601i
$141$	−34.3145	−	39.6011i	−0.243365	−	0.280859i
$142$	−77.7772	+	49.9844i	−0.547727	+	0.352003i
$143$	2.36155	−	0.339539i	0.0165143	−	0.00237440i
$144$	42.0331	+	27.0130i	0.291897	+	0.187590i
$145$	26.1804	+	11.9562i	0.180554	+	0.0824564i
$146$	94.6368	−	109.217i	0.648197	−	0.748059i
$147$	−5.16401	+	35.9165i	−0.0351293	+	0.244330i
$148$	−94.3197	+	43.0744i	−0.637295	+	0.291043i
$149$	−77.4937	+	263.919i	−0.520092	+	1.77127i	0.109110	+	0.994030i	$0.465200\pi$
$149$	−77.4937	+	263.919i	−0.520092	+	1.77127i	−0.629202	+	0.777242i	$0.716618\pi$
$150$	28.3701	+	8.33022i	0.189134	+	0.0555348i
$151$	−56.0266	−	122.681i	−0.371037	−	0.812458i	−0.999403	−	0.0345402i	$-0.989003\pi$
$151$	−56.0266	−	122.681i	−0.371037	−	0.812458i	0.628366	−	0.777918i	$-0.283724\pi$
$152$	−266.803	−	38.3604i	−1.75528	−	0.252371i
$153$	−146.788	−	127.193i	−0.959401	−	0.831325i
$154$	2.13260	−	4.66974i	0.0138481	−	0.0303230i
$155$	38.2910	−	59.5819i	0.247039	−	0.384400i
$156$	0.458563	+	3.18938i	0.00293951	+	0.0204447i
$157$	92.7142	+	144.266i	0.590536	+	0.918893i	0.999979	+	0.00655658i	$0.00208704\pi$
$157$	92.7142	+	144.266i	0.590536	+	0.918893i	−0.409442	+	0.912336i	$0.634277\pi$
$158$	24.8226	−	21.5089i	0.157105	−	0.136132i
$159$	10.1503	+	34.5687i	0.0638384	+	0.217413i
$160$			45.5298i			0.284561i
$161$	−60.0082	−	31.8765i	−0.372722	−	0.197991i
$162$	−90.0465			−0.555843
$163$	−44.0577	+	12.9365i	−0.270293	+	0.0793651i	−0.414070	−	0.910245i	$-0.635893\pi$
$163$	−44.0577	+	12.9365i	−0.270293	+	0.0793651i	0.143778	+	0.989610i	$0.454075\pi$
$164$	27.5173	+	31.7566i	0.167788	+	0.193638i
$165$	1.57019	−	1.00910i	0.00951630	−	0.00611575i
$166$	90.1146	−	12.9565i	0.542859	−	0.0780514i
$167$	−55.3091	−	35.5450i	−0.331192	−	0.212844i	0.364467	−	0.931216i	$-0.381251\pi$
$167$	−55.3091	−	35.5450i	−0.331192	−	0.212844i	−0.695659	+	0.718372i	$0.744888\pi$
$168$	20.9057	+	9.54729i	0.124438	+	0.0568291i
$169$	107.867	−	124.485i	0.638264	−	0.736596i
$170$	−9.14340	+	63.5937i	−0.0537847	+	0.374081i
$171$	232.530	−	106.193i	1.35982	−	0.621010i
$172$	−3.95192	+	13.4590i	−0.0229763	+	0.0782500i
$173$	101.039	+	29.6677i	0.584041	+	0.171490i	0.560388	−	0.828230i	$-0.310652\pi$
$173$	101.039	+	29.6677i	0.584041	+	0.171490i	0.0236529	+	0.999720i	$0.492470\pi$
$174$	9.03661	+	19.7874i	0.0519345	+	0.113721i
$175$	−63.6641	−	9.15351i	−0.363795	−	0.0523058i
$176$	5.31645	+	4.60673i	0.0302071	+	0.0261746i
$177$	17.1614	−	37.5782i	0.0969570	−	0.212306i
$178$	−57.0806	+	88.8191i	−0.320677	+	0.498984i
$179$	37.3674	+	259.896i	0.208756	+	1.45193i	0.777222	+	0.629226i	$0.216628\pi$
$179$	37.3674	+	259.896i	0.208756	+	1.45193i	−0.568466	+	0.822707i	$0.692463\pi$
$180$	−13.7456	−	21.3885i	−0.0763643	−	0.118825i
$181$	164.482	−	142.525i	0.908742	−	0.787430i	−0.0689176	−	0.997622i	$-0.521955\pi$
$181$	164.482	−	142.525i	0.908742	−	0.787430i	0.977660	+	0.210193i	$0.0674091\pi$
$182$	2.59641	+	8.84255i	0.0142660	+	0.0485854i
$183$		−	50.8597i		−	0.277922i
$184$	138.793	−	142.023i	0.754309	−	0.771864i
$185$	−107.825			−0.582840
$186$	51.3621	−	15.0813i	0.276140	−	0.0810821i
$187$	−17.9078	−	20.6667i	−0.0957635	−	0.110517i
$188$	−84.5403	+	54.3308i	−0.449682	+	0.288993i
$189$	−45.2874	+	6.51134i	−0.239616	+	0.0344515i
$190$	−71.1350	−	45.7157i	−0.374395	−	0.240609i
$191$	312.951	+	142.920i	1.63849	+	0.748272i	0.999776	−	0.0211747i	$-0.00674061\pi$
$191$	312.951	+	142.920i	1.63849	+	0.748272i	0.638711	+	0.769447i	$0.279468\pi$
$192$	−36.9369	+	42.6275i	−0.192380	+	0.222018i
$193$	15.1189	−	105.155i	0.0783365	−	0.544842i	−0.912427	−	0.409240i	$-0.865794\pi$
$193$	15.1189	−	105.155i	0.0783365	−	0.544842i	0.990763	−	0.135602i	$-0.0432970\pi$
$194$	−115.099	+	52.5639i	−0.593293	+	0.270948i
$195$	−0.943996	+	3.21496i	−0.00484101	+	0.0164870i
$196$	66.7708	+	19.6057i	0.340668	+	0.100029i
$197$	−59.9037	−	131.171i	−0.304080	−	0.665841i	0.694479	−	0.719513i	$-0.255635\pi$
$197$	−59.9037	−	131.171i	−0.304080	−	0.665841i	−0.998559	+	0.0536715i	$0.982908\pi$
$198$	−14.0836	−	2.02492i	−0.0711293	−	0.0102269i
$199$	−166.992	−	144.699i	−0.839156	−	0.727132i	0.125089	−	0.992145i	$-0.460078\pi$
$199$	−166.992	−	144.699i	−0.839156	−	0.727132i	−0.964245	+	0.265013i	$0.914624\pi$
$200$	78.0855	−	170.983i	0.390428	−	0.854917i
$201$	−38.8778	+	60.4950i	−0.193422	+	0.300970i
$202$	22.3174	+	155.221i	0.110482	+	0.768419i
$203$	−25.5829	−	39.8078i	−0.126024	−	0.196098i
$204$	27.9113	−	24.1853i	0.136820	−	0.118555i
$205$	12.3105	+	41.9259i	0.0600514	+	0.204516i
$206$			16.5989i			0.0805771i
$207$	−37.9126	+	184.472i	−0.183153	+	0.891170i
$208$	−12.6285			−0.0607139
$209$	34.5329	−	10.1398i	0.165229	−	0.0485157i
$210$	4.72139	+	5.44878i	0.0224828	+	0.0259466i
$211$	−22.6266	+	14.5412i	−0.107235	+	0.0689159i	−0.593159	−	0.805085i	$-0.702120\pi$
$211$	−22.6266	+	14.5412i	−0.107235	+	0.0689159i	0.485924	+	0.874001i	$0.338483\pi$
$212$	68.3922	−	9.83331i	0.322605	−	0.0463835i
$213$	46.4923	+	29.8788i	0.218274	+	0.140276i
$214$	−97.0788	−	44.3344i	−0.453639	−	0.207170i
$215$	−9.55221	+	11.0238i	−0.0444289	+	0.0512736i
$216$	19.0292	−	132.351i	0.0880982	−	0.612737i
$217$	−105.922	+	48.3728i	−0.488118	+	0.222916i
$218$	−63.8513	+	217.458i	−0.292896	+	0.997512i
$219$	−82.8861	−	24.3375i	−0.378475	−	0.111130i
$220$	−1.48701	−	3.25611i	−0.00675915	−	0.0148005i
$221$	48.5912	+	6.98636i	0.219870	+	0.0316125i
$222$	−61.5902	−	53.3682i	−0.277434	−	0.240398i
$223$	−47.7547	+	104.568i	−0.214147	+	0.468916i	−0.985970	−	0.166921i	$-0.946618\pi$
$223$	−47.7547	+	104.568i	−0.214147	+	0.468916i	0.771824	+	0.635837i	$0.219345\pi$
$224$	40.4702	−	62.9729i	0.180671	−	0.281129i
$225$	25.3698	+	176.451i	0.112755	+	0.784227i
$226$	−42.9995	−	66.9086i	−0.190263	−	0.296056i
$227$	−161.738	+	140.147i	−0.712501	+	0.617386i	−0.933790	−	0.357823i	$-0.883519\pi$
$227$	−161.738	+	140.147i	−0.712501	+	0.617386i	0.221288	+	0.975208i	$0.428974\pi$
$228$	13.6943	+	46.6384i	0.0600625	+	0.204554i
$229$		−	236.192i		−	1.03141i	−0.856767	−	0.515703i	$-0.827531\pi$
$229$		−	236.192i		−	1.03141i	0.856767	−	0.515703i	$-0.172469\pi$
$230$	58.1137	−	22.4400i	0.252668	−	0.0975654i
$231$	−3.06871			−0.0132845
$232$	132.689	−	38.9609i	0.571934	−	0.167935i
$233$	−186.988	−	215.796i	−0.802526	−	0.926164i	0.195991	−	0.980606i	$-0.437208\pi$
$233$	−186.988	−	215.796i	−0.802526	−	0.926164i	−0.998517	+	0.0544416i	$0.982662\pi$
$234$	21.4878	−	13.8094i	0.0918283	−	0.0590145i
$235$	−103.437	+	14.8721i	−0.440159	+	0.0632854i
$236$	−66.6507	−	42.8338i	−0.282418	−	0.181499i
$237$	−17.8593	−	8.15607i	−0.0753557	−	0.0344138i
$238$	69.1732	−	79.8301i	0.290644	−	0.335421i
$239$	−55.1209	+	383.374i	−0.230631	+	1.60408i	0.464755	+	0.885439i	$0.346142\pi$
$239$	−55.1209	+	383.374i	−0.230631	+	1.60408i	−0.695386	+	0.718636i	$0.744767\pi$
$240$	−8.98676	+	4.10411i	−0.0374448	+	0.0171005i
$241$	44.3533	−	151.054i	0.184039	−	0.626779i	−0.814851	−	0.579670i	$-0.803181\pi$
$241$	44.3533	−	151.054i	0.184039	−	0.626779i	0.998890	−	0.0471081i	$-0.0150005\pi$
$242$	173.076	+	50.8196i	0.715188	+	0.209998i
$243$	80.2616	+	175.748i	0.330295	+	0.723244i
$244$	−96.5469	−	13.8814i	−0.395684	−	0.0568908i
$245$	54.6899	+	47.3890i	0.223224	+	0.193425i
$246$	−13.7194	+	30.0413i	−0.0557700	+	0.122119i
$247$	−34.9308	+	54.3534i	−0.141420	+	0.220054i
$248$	−48.4306	−	336.842i	−0.195285	−	1.35823i
$249$	−29.4223	−	45.7819i	−0.118162	−	0.183863i
$250$	95.7384	−	82.9578i	0.382954	−	0.331831i
$251$	−43.2660	−	147.350i	−0.172374	−	0.587053i	−0.999680	−	0.0253010i	$-0.991946\pi$
$251$	−43.2660	−	147.350i	−0.172374	−	0.587053i	0.827305	−	0.561752i	$-0.189873\pi$
$252$			41.8008i			0.165876i
$253$	−8.97972	+	24.9483i	−0.0354930	+	0.0986097i
$254$	176.964			0.696709
$255$	36.8492	−	10.8199i	0.144507	−	0.0424310i
$256$	170.881	+	197.207i	0.667503	+	0.770339i
$257$	128.684	−	82.7001i	0.500715	−	0.321790i	−0.265787	−	0.964032i	$-0.585632\pi$
$257$	128.684	−	82.7001i	0.500715	−	0.321790i	0.766502	+	0.642242i	$0.221995\pi$
$258$	−10.9125	+	1.56898i	−0.0422966	+	0.00608133i
$259$	149.135	+	95.8431i	0.575810	+	0.370051i
$260$	5.84530	+	2.66946i	0.0224819	+	0.0102671i
$261$	−85.8856	+	99.1172i	−0.329063	+	0.379759i
$262$	33.6823	−	234.266i	0.128558	−	0.894144i
$263$	109.619	−	50.0613i	0.416802	−	0.190347i	−0.195965	−	0.980611i	$-0.562784\pi$
$263$	109.619	−	50.0613i	0.416802	−	0.190347i	0.612767	+	0.790264i	$0.290057\pi$
$264$	2.52664	−	8.60495i	0.00957061	−	0.0325945i
$265$	68.9407	+	20.2428i	0.260153	+	0.0763879i
$266$	57.7524	+	126.460i	0.217114	+	0.475414i
$267$	62.4691	+	8.98170i	0.233967	+	0.0336393i
$268$	104.226	+	90.3128i	0.388905	+	0.336988i
$269$	−22.4779	+	49.2197i	−0.0835609	+	0.182973i	−0.946800	−	0.321822i	$-0.895705\pi$
$269$	−22.4779	+	49.2197i	−0.0835609	+	0.182973i	0.863239	+	0.504795i	$0.168432\pi$
$270$	22.6779	−	35.2875i	0.0839922	−	0.130694i
$271$	−30.1358	−	209.599i	−0.111202	−	0.773428i	−0.966754	−	0.255710i	$-0.917691\pi$
$271$	−30.1358	−	209.599i	−0.111202	−	0.773428i	0.855551	−	0.517718i	$-0.173218\pi$
$272$	78.2553	+	121.768i	0.287703	+	0.447675i
$273$	4.16335	−	3.60756i	0.0152503	−	0.0132145i
$274$	−35.0284	−	119.296i	−0.127841	−	0.435386i
$275$			25.0984i			0.0912670i
$276$	−33.6938	−	12.1275i	−0.122079	−	0.0439403i
$277$	−171.584			−0.619435			−0.309718	−	0.950829i	$-0.600234\pi$
$277$	−171.584			−0.619435			−0.309718	+	0.950829i	$0.600234\pi$
$278$	−302.097	+	88.7038i	−1.08668	+	0.319078i
$279$	211.348	+	243.908i	0.757519	+	0.874224i
$280$	38.5582	−	24.7798i	0.137708	−	0.0884994i
$281$	181.958	−	26.1616i	0.647538	−	0.0931020i	0.189283	−	0.981923i	$-0.439384\pi$
$281$	181.958	−	26.1616i	0.647538	−	0.0931020i	0.458255	+	0.888821i	$0.348475\pi$
$282$	−66.4448	−	42.7015i	−0.235620	−	0.151424i
$283$	−300.250	−	137.119i	−1.06095	−	0.484521i	−0.193016	−	0.981196i	$-0.561827\pi$
$283$	−300.250	−	137.119i	−1.06095	−	0.484521i	−0.867937	+	0.496675i	$0.834554\pi$
$284$	69.4082	−	80.1014i	0.244395	−	0.282047i
$285$	−7.19342	+	50.0314i	−0.0252401	+	0.175549i
$286$	3.27122	−	1.49392i	0.0114378	−	0.00522349i
$287$	20.2399	−	68.9308i	0.0705223	−	0.240177i
$288$	−199.066	−	58.4512i	−0.691203	−	0.202956i
$289$	−113.687	−	248.939i	−0.393379	−	0.861381i
$290$	42.9410	+	6.17398i	0.148072	+	0.0212896i
$291$	57.1626	+	49.5317i	0.196435	+	0.170212i
$292$	−68.8224	+	150.700i	−0.235693	+	0.516096i
$293$	22.3672	−	34.8040i	0.0763385	−	0.118785i	−0.800985	−	0.598684i	$-0.795690\pi$
$293$	22.3672	−	34.8040i	0.0763385	−	0.118785i	0.877324	+	0.479899i	$0.159327\pi$
$294$	7.78381	+	54.1376i	0.0264756	+	0.184142i
$295$	−44.5421	−	69.3089i	−0.150990	−	0.234945i
$296$	−391.544	+	339.275i	−1.32278	+	1.14620i
$297$	5.02998	+	17.1305i	0.0169359	+	0.0576785i
$298$			414.605i			1.39129i
$299$	−17.1462	−	44.4040i	−0.0573450	−	0.148508i
$300$	−33.8966			−0.112989
$301$	23.0106	−	6.75652i	0.0764471	−	0.0224469i
$302$	−133.127	−	153.637i	−0.440818	−	0.508731i
$303$	78.8585	−	50.6792i	0.260259	−	0.167258i
$304$	−188.565	+	27.1115i	−0.620279	+	0.0891827i
$305$	−85.3282	−	54.8371i	−0.279765	−	0.179794i
$306$	−266.308	−	121.619i	−0.870288	−	0.397447i
$307$	−94.1590	+	108.665i	−0.306707	+	0.353958i	−0.888089	−	0.459672i	$-0.847967\pi$
$307$	−94.1590	+	108.665i	−0.306707	+	0.353958i	0.581382	+	0.813631i	$0.302512\pi$
$308$	−0.837557	+	5.82533i	−0.00271934	+	0.0189134i
$309$	9.02555	−	4.12183i	0.0292089	−	0.0133393i
$310$	30.0767	−	102.432i	0.0970215	−	0.330425i
$311$	−517.824	−	152.047i	−1.66503	−	0.488897i	−0.692450	−	0.721466i	$-0.743469\pi$
$311$	−517.824	−	152.047i	−1.66503	−	0.488897i	−0.972580	+	0.232569i	$0.925287\pi$
$312$	6.68801	+	14.6447i	0.0214359	+	0.0469382i
$313$	512.701	+	73.7153i	1.63802	+	0.235512i	0.898930	−	0.438092i	$-0.144346\pi$
$313$	512.701	+	73.7153i	1.63802	+	0.235512i	0.739093	+	0.673604i	$0.235255\pi$
$314$	195.353	+	169.274i	0.622144	+	0.539091i
$315$	−18.0572	+	39.5398i	−0.0573245	+	0.125523i
$316$	−20.3571	+	31.6762i	−0.0644211	+	0.100241i
$317$	−57.4286	−	399.425i	−0.181163	−	1.26001i	−0.854019	−	0.520242i	$-0.825842\pi$
$317$	−57.4286	−	399.425i	−0.181163	−	1.26001i	0.672856	−	0.739773i	$-0.265067\pi$
$318$	29.3600	+	45.6850i	0.0923270	+	0.143664i
$319$	−13.9549	+	12.0920i	−0.0437459	+	0.0379060i
$320$	31.6913	+	107.931i	0.0990354	+	0.337284i
$321$			63.7951i			0.198739i
$322$	−100.324	−	20.6186i	−0.311566	−	0.0640329i
$323$	740.548			2.29272
$324$	99.0479	−	29.0831i	0.305703	−	0.0897626i
$325$	−29.5055	−	34.0512i	−0.0907863	−	0.104773i
$326$	−58.2253	+	37.4191i	−0.178605	+	0.114783i
$327$	134.097	−	19.2802i	0.410082	−	0.0589609i
$328$	176.624	+	113.509i	0.538487	+	0.346064i
$329$	156.285	+	71.3731i	0.475031	+	0.216939i
$330$	1.84238	−	2.12622i	0.00558297	−	0.00644309i
$331$	−16.6862	+	116.055i	−0.0504114	+	0.350619i	0.948967	+	0.315374i	$0.102130\pi$
$331$	−16.6862	+	116.055i	−0.0504114	+	0.350619i	−0.999379	+	0.0352446i	$0.988779\pi$
$332$	−94.9382	+	43.3568i	−0.285958	+	0.130593i
$333$	138.426	−	471.437i	0.415695	−	1.41573i
$334$	−95.0860	−	27.9198i	−0.284689	−	0.0835921i
$335$	59.5753	+	130.452i	0.177837	+	0.389408i
$336$	16.0778	+	2.31163i	0.0478505	+	0.00687986i
$337$	344.774	+	298.748i	1.02307	+	0.886494i	0.993587	−	0.113071i	$-0.0360689\pi$
$337$	344.774	+	298.748i	1.02307	+	0.886494i	0.0294816	+	0.999565i	$0.490614\pi$
$338$	103.140	−	225.844i	0.305147	−	0.668178i
$339$	−25.7035	+	39.9954i	−0.0758216	+	0.117981i
$340$	−10.4820	−	72.9039i	−0.0308294	−	0.214423i
$341$	24.5661	+	38.2256i	0.0720414	+	0.112099i
$342$	291.203	−	252.329i	0.851470	−	0.737803i
$343$	−74.3035	−	253.054i	−0.216628	−	0.737768i
$344$			70.0868i			0.203741i
$345$	−26.6324	−	26.0267i	−0.0771954	−	0.0754397i
$346$	158.728			0.458750
$347$	−118.981	+	34.9359i	−0.342884	+	0.100680i	−0.448641	−	0.893712i	$-0.648092\pi$
$347$	−118.981	+	34.9359i	−0.342884	+	0.100680i	0.105757	+	0.994392i	$0.466274\pi$
$348$	−16.3309	−	18.8468i	−0.0469277	−	0.0541575i
$349$	32.6130	−	20.9591i	0.0934470	−	0.0600548i	−0.493083	−	0.869982i	$-0.664130\pi$
$349$	32.6130	−	20.9591i	0.0934470	−	0.0600548i	0.586530	+	0.809928i	$0.300494\pi$
$350$	−95.9621	+	13.7973i	−0.274177	+	0.0394207i
$351$	−26.9627	−	17.3279i	−0.0768169	−	0.0493672i
$352$	−26.5706	−	12.1344i	−0.0754846	−	0.0344727i
$353$	−243.662	+	281.201i	−0.690261	+	0.796604i	−0.987402	−	0.158230i	$-0.949421\pi$
$353$	−243.662	+	281.201i	−0.690261	+	0.796604i	0.297141	+	0.954834i	$0.403967\pi$
$354$	8.86187	−	61.6357i	0.0250335	−	0.174112i
$355$	100.256	−	45.7855i	0.282412	−	0.128973i
$356$	34.0999	−	116.134i	0.0957862	−	0.326218i
$357$	−60.5842	−	17.7891i	−0.169704	−	0.0498295i
$358$	164.411	+	360.009i	0.459248	+	1.00561i
$359$	−219.319	−	31.5333i	−0.610917	−	0.0878365i	−0.170090	−	0.985429i	$-0.554406\pi$
$359$	−219.319	−	31.5333i	−0.610917	−	0.0878365i	−0.440827	+	0.897592i	$0.645315\pi$
$360$	−96.0058	−	83.1895i	−0.266683	−	0.231082i
$361$	−254.923	+	558.203i	−0.706157	+	1.54627i
$362$	177.360	−	275.977i	0.489944	−	0.762368i
$363$	−15.3452	−	106.728i	−0.0422733	−	0.294017i
$364$	−5.71191	−	8.88790i	−0.0156921	−	0.0244173i
$365$	−130.200	+	112.819i	−0.356711	+	0.309092i
$366$	−21.5981	−	73.5564i	−0.0590113	−	0.200974i
$367$		−	154.773i		−	0.421725i	−0.977516	−	0.210862i	$-0.932373\pi$
$367$		−	154.773i		−	0.421725i	0.977516	−	0.210862i	$-0.0676272\pi$
$368$	65.8403	−	123.946i	0.178914	−	0.336809i
$369$	−199.114			−0.539604
$370$	−155.944	+	45.7892i	−0.421469	+	0.123755i
$371$	−77.3595	−	89.2776i	−0.208516	−	0.240641i
$372$	−51.6255	+	33.1777i	−0.138778	+	0.0891874i
$373$	−264.336	+	38.0058i	−0.708677	+	0.101892i	−0.487222	−	0.873278i	$-0.661990\pi$
$373$	−264.336	+	38.0058i	−0.708677	+	0.101892i	−0.221455	+	0.975171i	$0.571081\pi$
$374$	−34.6756	−	22.2847i	−0.0927156	−	0.0595847i
$375$	−68.8816	−	31.4572i	−0.183684	−	0.0838857i
$376$	−328.815	+	379.473i	−0.874508	+	1.00924i
$377$	4.71746	−	32.8107i	0.0125132	−	0.0870310i
$378$	−62.7322	+	28.6489i	−0.165958	+	0.0757906i
$379$	67.5940	−	230.204i	0.178348	−	0.607399i	−0.820987	−	0.570947i	$-0.806576\pi$
$379$	67.5940	−	230.204i	0.178348	−	0.607399i	0.999335	−	0.0364518i	$-0.0116056\pi$
$380$	93.0112	+	27.3105i	0.244766	+	0.0718698i
$381$	−43.9436	−	96.2232i	−0.115338	−	0.252554i
$382$	513.301	+	73.8016i	1.34372	+	0.193198i
$383$	316.026	+	273.838i	0.825133	+	0.714982i	0.961240	−	0.275712i	$-0.0889136\pi$
$383$	316.026	+	273.838i	0.825133	+	0.714982i	−0.136107	+	0.990694i	$0.543459\pi$
$384$	2.61726	−	5.73100i	0.00681579	−	0.0149245i
$385$	−3.30870	+	5.14843i	−0.00859401	+	0.0133725i
$386$	−22.7891	−	158.501i	−0.0590390	−	0.410625i
$387$	−35.9356	−	55.9168i	−0.0928568	−	0.144488i
$388$	109.628	−	94.9929i	0.282545	−	0.244827i
$389$	−4.65034	−	15.8376i	−0.0119546	−	0.0407137i	0.953300	−	0.302026i	$-0.0976629\pi$
$389$	−4.65034	−	15.8376i	−0.0119546	−	0.0407137i	−0.965254	+	0.261312i	$0.915845\pi$
$390$			5.05055i			0.0129501i
$391$	−321.906	+	440.487i	−0.823289	+	1.12657i
$392$	347.705			0.887002
$393$	−135.745	+	39.8582i	−0.345406	+	0.101420i
$394$	−142.339	−	164.268i	−0.361268	−	0.416925i
$395$	−32.9395	+	21.1689i	−0.0833912	+	0.0535923i
$396$	16.1455	−	2.32137i	0.0407714	−	0.00586204i
$397$	131.195	+	84.3139i	0.330466	+	0.212378i	0.695343	−	0.718678i	$-0.255253\pi$
$397$	131.195	+	84.3139i	0.330466	+	0.212378i	−0.364877	+	0.931056i	$0.618889\pi$
$398$	−302.962	−	138.358i	−0.761211	−	0.347634i
$399$	54.4209	−	62.8050i	0.136393	−	0.157406i
$400$	18.9064	−	131.497i	0.0472660	−	0.328742i
$401$	−440.307	+	201.081i	−1.09802	+	0.501450i	−0.880231	−	0.474546i	$-0.842612\pi$
$401$	−440.307	+	201.081i	−1.09802	+	0.501450i	−0.217791	+	0.975996i	$0.569885\pi$
$402$	−30.5376	+	104.001i	−0.0759641	+	0.258710i
$403$	−78.2668	−	22.9812i	−0.194211	−	0.0570254i
$404$	−74.6812	−	163.529i	−0.184854	−	0.404775i
$405$	106.254	+	15.2770i	0.262355	+	0.0377210i
$406$	−53.9044	−	46.7084i	−0.132769	−	0.115045i
$407$	28.7371	−	62.9255i	0.0706071	−	0.154608i
$408$	99.7647	−	155.237i	0.244521	−	0.380483i
$409$	−12.5414	−	87.2271i	−0.0306635	−	0.213269i	0.968729	−	0.248121i	$-0.0798131\pi$
$409$	−12.5414	−	87.2271i	−0.0306635	−	0.213269i	−0.999392	+	0.0348520i	$0.988904\pi$
$410$	35.6085	+	55.4080i	0.0868501	+	0.135141i
$411$	−56.1681	+	48.6699i	−0.136662	+	0.118418i
$412$	−5.36108	−	18.2582i	−0.0130123	−	0.0443160i
$413$			135.454i			0.327977i
$414$	23.5065	+	282.895i	0.0567790	+	0.683321i
$415$	−108.532			−0.261524
$416$	50.3136	−	14.7734i	0.120946	−	0.0355130i
$417$	123.249	+	142.237i	0.295561	+	0.341095i
$418$	45.6377	−	29.3296i	0.109181	−	0.0701664i
$419$	364.656	−	52.4296i	0.870301	−	0.125130i	0.307326	−	0.951604i	$-0.400566\pi$
$419$	364.656	−	52.4296i	0.870301	−	0.125130i	0.562975	+	0.826474i	$0.309657\pi$
$420$	−6.95320	−	4.46855i	−0.0165552	−	0.0106394i
$421$	57.9144	+	26.4486i	0.137564	+	0.0628233i	0.483008	−	0.875616i	$-0.339544\pi$
$421$	57.9144	+	26.4486i	0.137564	+	0.0628233i	−0.345444	+	0.938439i	$0.612272\pi$
$422$	−26.5489	+	30.6391i	−0.0629121	+	0.0726045i
$423$	67.7692	−	471.345i	0.160211	−	1.11429i
$424$	314.037	−	143.416i	0.740654	−	0.338245i
$425$	−145.494	+	495.507i	−0.342339	+	1.16590i
$426$	79.9284	+	23.4691i	0.187625	+	0.0550918i
$427$	69.2754	+	151.692i	0.162237	+	0.355251i
$428$	121.102	+	17.4119i	0.282949	+	0.0406819i
$429$	−1.62462	−	1.40774i	−0.00378699	−	0.00328144i
$430$	−9.13360	+	19.9998i	−0.0212409	+	0.0465111i
$431$	386.037	−	600.686i	0.895678	−	1.39370i	−0.0234421	−	0.999725i	$-0.507463\pi$
$431$	386.037	−	600.686i	0.895678	−	1.39370i	0.919120	−	0.393977i	$-0.128901\pi$
$432$	−13.4490	−	93.5402i	−0.0311320	−	0.216528i
$433$	348.866	+	542.846i	0.805695	+	1.25369i	0.963896	+	0.266279i	$0.0857943\pi$
$433$	348.866	+	542.846i	0.805695	+	1.25369i	−0.158201	+	0.987407i	$0.550569\pi$
$434$	−132.648	+	114.940i	−0.305641	+	0.264840i
$435$	−7.30602	−	24.8820i	−0.0167955	−	0.0572001i
$436$		−	259.818i		−	0.595913i
$437$	−351.350	−	626.216i	−0.804005	−	1.43299i
$438$	−130.210			−0.297283
$439$	40.7516	−	11.9658i	0.0928283	−	0.0272569i	−0.234989	−	0.971998i	$-0.575505\pi$
$439$	40.7516	−	11.9658i	0.0928283	−	0.0272569i	0.327817	+	0.944741i	$0.393687\pi$
$440$	−11.7124	−	13.5169i	−0.0266192	−	0.0307202i
$441$	−277.407	+	178.278i	−0.629040	+	0.404260i
$442$	73.2424	−	10.5307i	0.165707	−	0.0238250i
$443$	−555.635	−	357.085i	−1.25425	−	0.806061i	−0.266768	−	0.963761i	$-0.585956\pi$
$443$	−555.635	−	357.085i	−1.25425	−	0.806061i	−0.987487	+	0.157700i	$0.949592\pi$
$444$	84.9838	+	38.8108i	0.191405	+	0.0874118i
$445$	82.4231	−	95.1213i	0.185220	−	0.213756i
$446$	−24.6598	+	171.513i	−0.0552910	+	0.384557i
$447$	225.439	−	102.955i	0.504338	−	0.230323i
$448$	52.1041	−	177.450i	0.116304	−	0.396094i
$449$	709.638	+	208.369i	1.58049	+	0.464073i	0.950032	−	0.312153i	$-0.101050\pi$
$449$	709.638	+	208.369i	1.58049	+	0.464073i	0.630455	+	0.776226i	$0.282868\pi$
$450$	111.623	+	244.421i	0.248052	+	0.543157i
$451$	−27.7483	−	3.98961i	−0.0615263	−	0.00884614i
$452$	68.9079	+	59.7091i	0.152451	+	0.132100i
$453$	−50.4810	+	110.538i	−0.111437	+	0.244013i
$454$	−174.400	+	271.372i	−0.384142	+	0.597736i
$455$	−1.56353	−	10.8746i	−0.00343633	−	0.0239002i
$456$	131.303	+	204.312i	0.287946	+	0.448053i
$457$	324.728	−	281.378i	0.710565	−	0.615708i	−0.222704	−	0.974886i	$-0.571488\pi$
$457$	324.728	−	281.378i	0.710565	−	0.615708i	0.933269	+	0.359178i	$0.116943\pi$
$458$	−100.301	−	341.595i	−0.218999	−	0.745841i
$459$			367.359i			0.800346i
$460$	−56.6753	+	43.4527i	−0.123207	+	0.0944624i
$461$	7.25384			0.0157350			0.00786750	−	0.999969i	$-0.497496\pi$
$461$	7.25384			0.0157350			0.00786750	+	0.999969i	$0.497496\pi$
$462$	−4.43816	+	1.30316i	−0.00960641	+	0.00282070i
$463$	150.300	+	173.455i	0.324622	+	0.374634i	0.894479	−	0.447110i	$-0.147547\pi$
$463$	150.300	+	173.455i	0.324622	+	0.374634i	−0.569857	+	0.821744i	$0.693001\pi$
$464$	82.2223	−	52.8410i	0.177203	−	0.113882i
$465$	−63.1653	+	9.08180i	−0.135839	+	0.0195307i
$466$	−362.074	−	232.691i	−0.776984	−	0.499337i
$467$	542.034	+	247.539i	1.16067	+	0.530062i	0.900225	−	0.435426i	$-0.143402\pi$
$467$	542.034	+	247.539i	1.16067	+	0.530062i	0.260449	+	0.965488i	$0.416130\pi$
$468$	−19.1757	+	22.1299i	−0.0409737	+	0.0472862i
$469$	33.5556	−	233.385i	0.0715472	−	0.497622i
$470$	−143.282	+	65.4347i	−0.304855	+	0.139223i
$471$	43.5320	−	148.256i	0.0924246	−	0.314769i
$472$	−379.827	−	111.527i	−0.804718	−	0.236286i
$473$	−3.88756	−	8.51256i	−0.00821894	−	0.0179970i
$474$	−29.2928	−	4.21167i	−0.0617991	−	0.00888537i
$475$	−513.671	−	445.098i	−1.08141	−	0.937049i
$476$	−50.3046	+	110.152i	−0.105682	+	0.231411i
$477$	−177.012	+	275.437i	−0.371095	+	0.577435i
$478$	83.0847	+	577.867i	0.173817	+	1.20893i
$479$	−120.803	−	187.972i	−0.252197	−	0.392427i	0.691953	−	0.721943i	$-0.256751\pi$
$479$	−120.803	−	187.972i	−0.252197	−	0.392427i	−0.944150	+	0.329516i	$0.893114\pi$
$480$	31.0032	−	26.8645i	0.0645901	−	0.0559676i
$481$	34.9870	+	119.155i	0.0727379	+	0.247723i
$482$		−	237.298i		−	0.492320i
$483$	13.7012	+	59.6707i	0.0283670	+	0.123542i
$484$	−206.790			−0.427253
$485$	144.733	−	42.4975i	0.298419	−	0.0876237i
$486$	190.713	+	220.094i	0.392413	+	0.452868i
$487$	−448.376	+	288.154i	−0.920690	+	0.591691i	−0.912858	−	0.408278i	$-0.866129\pi$
$487$	−448.376	+	288.154i	−0.920690	+	0.591691i	−0.00783211	+	0.999969i	$0.502493\pi$
$488$	−482.397	+	69.3582i	−0.988518	+	0.142127i
$489$	34.8049	+	22.3678i	0.0711757	+	0.0457419i
$490$	99.2201	+	45.3123i	0.202490	+	0.0924741i
$491$	−87.3058	+	100.756i	−0.177812	+	0.205206i	−0.837658	−	0.546194i	$-0.816076\pi$
$491$	−87.3058	+	100.756i	−0.177812	+	0.205206i	0.659846	+	0.751401i	$0.270621\pi$
$492$	5.38816	−	37.4755i	0.0109515	−	0.0761696i
$493$	−345.603	+	157.832i	−0.701020	+	0.320145i
$494$	−27.4373	+	93.4430i	−0.0555412	+	0.189156i
$495$	16.2749	+	4.77876i	0.0328787	+	0.00965405i
$496$	−99.9131	−	218.779i	−0.201438	−	0.441087i
$497$	−179.364	−	25.7886i	−0.360892	−	0.0518885i
$498$	−61.9941	−	53.7182i	−0.124486	−	0.107868i
$499$	282.054	−	617.611i	0.565238	−	1.23770i	−0.384057	−	0.923310i	$-0.625473\pi$
$499$	282.054	−	617.611i	0.565238	−	1.23770i	0.949294	−	0.314389i	$-0.101799\pi$
$500$	−78.5152	+	122.172i	−0.157030	+	0.244344i
$501$	8.43051	+	58.6355i	0.0168274	+	0.117037i
$502$	−125.148	−	194.734i	−0.249298	−	0.387916i
$503$	−221.840	+	192.225i	−0.441033	+	0.382157i	−0.846880	−	0.531784i	$-0.821522\pi$
$503$	−221.840	+	192.225i	−0.441033	+	0.382157i	0.405847	+	0.913941i	$0.366977\pi$
$504$	58.8420	+	200.398i	0.116750	+	0.397614i
$505$		−	186.945i		−	0.370188i
$506$	−2.39247	+	39.8950i	−0.00472821	+	0.0788439i
$507$	−148.413			−0.292728
$508$	−194.654	+	57.1556i	−0.383177	+	0.112511i
$509$	−342.418	−	395.171i	−0.672727	−	0.776368i	0.312074	−	0.950058i	$-0.398976\pi$
$509$	−342.418	−	395.171i	−0.672727	−	0.776368i	−0.984800	+	0.173690i	$0.944431\pi$
$510$	48.6988	−	31.2968i	0.0954878	−	0.0613663i
$511$	280.362	−	40.3100i	0.548654	−	0.0788846i
$512$	307.354	+	197.525i	0.600301	+	0.385790i
$513$	−439.800	−	200.850i	−0.857310	−	0.391520i
$514$	150.991	−	174.253i	0.293757	−	0.339014i
$515$	2.81611	−	19.5865i	0.00546818	−	0.0380320i
$516$	11.4966	−	5.25033i	0.0222803	−	0.0101751i
$517$	18.8885	−	64.3284i	0.0365349	−	0.124426i
$518$	256.389	+	75.2825i	0.494959	+	0.145333i
$519$	−39.4152	−	86.3072i	−0.0759444	−	0.166295i
$520$	31.7807	+	4.56938i	0.0611168	+	0.00878726i
$521$	286.390	+	248.158i	0.549692	+	0.476311i	0.884866	−	0.465845i	$-0.154250\pi$
$521$	286.390	+	248.158i	0.549692	+	0.476311i	−0.335174	+	0.942156i	$0.608795\pi$
$522$	−82.1218	+	179.822i	−0.157321	+	0.344486i
$523$	358.489	−	557.820i	0.685448	−	1.06658i	−0.307899	−	0.951419i	$-0.599626\pi$
$523$	358.489	−	557.820i	0.685448	−	1.06658i	0.993347	−	0.115159i	$-0.0367376\pi$
$524$	38.6134	+	268.562i	0.0736898	+	0.512524i
$525$	31.3314	+	48.7527i	0.0596789	+	0.0928622i
$526$	137.279	−	118.953i	0.260986	−	0.226146i
$527$	263.406	+	897.079i	0.499822	+	1.70224i
$528$		−	6.33837i		−	0.0120045i
$529$	525.209	+	63.2200i	0.992833	+	0.119509i
$530$	108.303			0.204344
$531$	360.218	−	105.769i	0.678376	−	0.199189i
$532$	−104.369	−	120.449i	−0.196183	−	0.226407i
$533$	42.3365	−	27.2080i	0.0794307	−	0.0510470i
$534$	94.1608	−	13.5383i	0.176331	−	0.0253526i
$535$	107.030	+	68.7841i	0.200056	+	0.128568i
$536$	626.804	+	286.252i	1.16941	+	0.534052i
$537$	154.926	−	178.795i	0.288504	−	0.332951i
$538$	−11.6072	+	80.7300i	−0.0215748	+	0.150056i
$539$	−42.2313	+	19.2864i	−0.0783513	+	0.0357818i
$540$	−13.5478	+	46.1394i	−0.0250884	+	0.0854434i
$541$	174.384	+	51.2037i	0.322336	+	0.0946464i	0.438898	−	0.898537i	$-0.355369\pi$
$541$	174.384	+	51.2037i	0.322336	+	0.0946464i	−0.116562	+	0.993183i	$0.537187\pi$
$542$	−132.593	−	290.337i	−0.244636	−	0.535678i
$543$	−194.103	−	27.9078i	−0.357464	−	0.0513956i
$544$	−454.229	−	393.591i	−0.834979	−	0.723514i
$545$	112.237	−	245.765i	0.205939	−	0.450944i
$546$	4.48930	−	6.98548i	0.00822216	−	0.0127939i
$547$	25.0559	+	174.268i	0.0458061	+	0.318588i	0.999823	+	0.0188343i	$0.00599551\pi$
$547$	25.0559	+	174.268i	0.0458061	+	0.318588i	−0.954017	+	0.299754i	$0.903095\pi$
$548$	77.0599	+	119.908i	0.140620	+	0.218809i
$549$	349.305	−	302.674i	0.636257	−	0.551319i
$550$	10.6583	+	36.2989i	0.0193788	+	0.0659980i
$551$		−	500.047i		−	0.907526i
$552$	−178.603	−	10.7107i	−0.323557	−	0.0194034i
$553$	64.3757			0.116412
$554$	−248.155	+	72.8648i	−0.447932	+	0.131525i
$555$	63.6215	+	73.4231i	0.114633	+	0.132294i
$556$	303.647	−	195.142i	0.546127	−	0.350975i
$557$	38.9953	−	5.60668i	0.0700095	−	0.0100659i	−0.107221	−	0.994235i	$-0.534195\pi$
$557$	38.9953	−	5.60668i	0.0700095	−	0.0100659i	0.177231	+	0.984169i	$0.443286\pi$
$558$	409.242	+	263.004i	0.733409	+	0.471334i
$559$	15.2816	+	6.97887i	0.0273374	+	0.0124846i
$560$	21.2133	−	24.4815i	0.0378810	−	0.0437170i
$561$	−3.50652	+	24.3884i	−0.00625048	+	0.0434731i
$562$	252.049	−	115.107i	0.448486	−	0.204817i
$563$	−263.714	+	898.127i	−0.468408	+	1.59525i	0.299106	+	0.954220i	$0.403311\pi$
$563$	−263.714	+	898.127i	−0.468408	+	1.59525i	−0.767514	+	0.641032i	$0.778507\pi$
$564$	86.8785	+	25.5098i	0.154040	+	0.0452302i
$565$	39.3874	+	86.2464i	0.0697123	+	0.152649i
$566$	−492.469	−	70.8063i	−0.870086	−	0.125099i
$567$	−133.382	−	115.576i	−0.235241	−	0.203838i
$568$	219.994	−	481.719i	0.387313	−	0.848096i
$569$	−564.024	+	877.639i	−0.991255	+	1.54242i	−0.159561	+	0.987188i	$0.551008\pi$
$569$	−564.024	+	877.639i	−0.991255	+	1.54242i	−0.831694	+	0.555235i	$0.812628\pi$
$570$	10.8428	+	75.4132i	0.0190224	+	0.132304i
$571$	−358.267	−	557.474i	−0.627437	−	0.976312i	−0.998855	−	0.0478455i	$-0.984764\pi$
$571$	−358.267	−	557.474i	−0.627437	−	0.976312i	0.371417	−	0.928466i	$-0.378872\pi$
$572$	−3.11572	+	2.69979i	−0.00544707	+	0.00471991i
$573$	−87.3336	−	297.431i	−0.152415	−	0.519077i
$574$		−	108.287i		−	0.188653i
$575$	488.036	−	112.060i	0.848758	−	0.194887i
$576$	−512.583			−0.889902
$577$	252.960	−	74.2758i	0.438406	−	0.128728i	−0.0550789	−	0.998482i	$-0.517541\pi$
$577$	252.960	−	74.2758i	0.438406	−	0.128728i	0.493485	+	0.869754i	$0.335723\pi$
$578$	−270.135	−	311.753i	−0.467362	−	0.539365i
$579$	−80.5252	+	51.7504i	−0.139076	+	0.0893790i
$580$	−49.2276	+	7.07786i	−0.0848752	+	0.0122032i
$581$	150.113	+	96.4715i	0.258369	+	0.166044i
$582$	103.706	+	47.3611i	0.178189	+	0.0813764i
$583$	−30.1872	+	34.8379i	−0.0517790	+	0.0597562i
$584$	−117.805	+	819.351i	−0.201721	+	1.40300i
$585$	−27.6982	+	12.6494i	−0.0473474	+	0.0216228i
$586$	17.5689	−	59.8342i	0.0299811	−	0.102106i
$587$	−239.683	−	70.3774i	−0.408319	−	0.119893i	0.0711213	−	0.997468i	$-0.477342\pi$
$587$	−239.683	−	70.3774i	−0.408319	−	0.119893i	−0.479441	+	0.877574i	$0.659160\pi$
$588$	−26.0472	−	57.0354i	−0.0442980	−	0.0969990i
$589$	−1217.99	−	175.121i	−2.06790	−	0.297319i
$590$	−93.8523	−	81.3235i	−0.159072	−	0.137836i
$591$	−53.9743	+	118.187i	−0.0913271	+	0.199979i
$592$	−197.962	+	308.035i	−0.334395	+	0.520329i
$593$	−19.6840	−	136.905i	−0.0331939	−	0.230869i	0.966470	−	0.256778i	$-0.0826610\pi$
$593$	−19.6840	−	136.905i	−0.0331939	−	0.230869i	−0.999664	+	0.0259093i	$0.991752\pi$
$594$	14.5493	+	22.6392i	0.0244938	+	0.0381131i
$595$	−95.1672	+	82.4628i	−0.159945	+	0.138593i
$596$	−133.909	−	456.051i	−0.224679	−	0.765186i
$597$			199.091i			0.333486i
$598$	−43.6545	−	56.9385i	−0.0730008	−	0.0952148i
$599$	−142.251			−0.237481			−0.118740	−	0.992925i	$-0.537886\pi$
$599$	−142.251			−0.237481			−0.118740	+	0.992925i	$0.537886\pi$
$600$	−162.504	+	47.7155i	−0.270840	+	0.0795258i
$601$	446.927	+	515.781i	0.743638	+	0.858204i	0.993935	−	0.109965i	$-0.0350738\pi$
$601$	446.927	+	515.781i	0.743638	+	0.858204i	−0.250297	+	0.968169i	$0.580528\pi$
$602$	30.4101	−	19.5434i	0.0505151	−	0.0324641i
$603$	−646.848	+	93.0027i	−1.07272	+	0.154233i
$604$	196.056	+	125.998i	0.324596	+	0.208605i
$605$	−195.605	−	89.3299i	−0.323314	−	0.147653i
$606$	92.5284	−	106.784i	0.152687	−	0.176210i
$607$	−37.6089	+	261.576i	−0.0619587	+	0.430932i	0.935106	+	0.354368i	$0.115304\pi$
$607$	−37.6089	+	261.576i	−0.0619587	+	0.430932i	−0.997065	+	0.0765640i	$0.975605\pi$
$608$	719.551	−	328.608i	1.18347	−	0.540473i
$609$	−12.0119	+	40.9088i	−0.0197240	+	0.0671738i
$610$	−146.694	−	43.0733i	−0.240482	−	0.0706119i
$611$	49.9979	+	109.480i	0.0818296	+	0.179182i
$612$	332.209	+	47.7645i	0.542826	+	0.0780466i
$613$	12.3304	+	10.6844i	0.0201148	+	0.0174296i	0.664860	−	0.746968i	$-0.268491\pi$
$613$	12.3304	+	10.6844i	0.0201148	+	0.0174296i	−0.644745	+	0.764397i	$0.723037\pi$
$614$	−90.0326	+	197.144i	−0.146633	+	0.321081i
$615$	21.2855	−	33.1208i	0.0346105	−	0.0538550i
$616$	4.18485	+	29.1063i	0.00679359	+	0.0472504i
$617$	−217.402	−	338.284i	−0.352353	−	0.548272i	0.619158	−	0.785267i	$-0.287474\pi$
$617$	−217.402	−	338.284i	−0.352353	−	0.548272i	−0.971511	+	0.236994i	$0.923838\pi$
$618$	11.3029	−	9.79404i	0.0182895	−	0.0158480i
$619$	186.666	+	635.726i	0.301561	+	1.02702i	0.961295	+	0.275522i	$0.0888507\pi$
$619$	186.666	+	635.726i	0.301561	+	1.02702i	−0.659734	+	0.751499i	$0.729331\pi$
$620$			122.385i			0.197396i
$621$	310.643	−	174.292i	0.500230	−	0.280663i
$622$	−813.478			−1.30784
$623$	−198.551	+	58.3000i	−0.318702	+	0.0935794i
$624$	7.45134	+	8.59931i	0.0119413	+	0.0137809i
$625$	330.831	−	212.612i	0.529330	−	0.340180i
$626$	772.804	−	111.112i	1.23451	−	0.177496i
$627$	−27.2805	−	17.5321i	−0.0435096	−	0.0279619i
$628$	−269.553	−	123.101i	−0.429225	−	0.196021i
$629$	932.118	−	1075.72i	1.48191	−	1.71021i
$630$	−9.32447	+	64.8531i	−0.0148007	+	0.102941i
$631$	354.889	−	162.072i	0.562423	−	0.256850i	−0.113854	−	0.993498i	$-0.536320\pi$
$631$	354.889	−	162.072i	0.562423	−	0.256850i	0.676277	+	0.736647i	$0.263592\pi$
$632$	−53.0041	+	180.515i	−0.0838672	+	0.285625i
$633$	23.2524	+	6.82753i	0.0367337	+	0.0107860i
$634$	−252.677	−	553.285i	−0.398544	−	0.872689i
$635$	−208.815	−	30.0231i	−0.328843	−	0.0472805i
$636$	−47.0502	−	40.7692i	−0.0739783	−	0.0641025i
$637$	34.6226	−	75.8129i	0.0543526	−	0.119016i
$638$	−15.0475	+	23.4143i	−0.0235854	+	0.0366996i
$639$	71.4755	+	497.123i	0.111855	+	0.777970i
$640$	−6.79306	−	10.5702i	−0.0106142	−	0.0165160i
$641$	−398.084	+	344.942i	−0.621037	+	0.538131i	−0.907549	−	0.419945i	$-0.862049\pi$
$641$	−398.084	+	344.942i	−0.621037	+	0.538131i	0.286513	+	0.958076i	$0.407504\pi$
$642$	27.0913	+	92.2644i	0.0421983	+	0.143714i
$643$			1242.86i			1.93291i	0.256828	+	0.966457i	$0.417323\pi$
$643$			1242.86i			1.93291i	−0.256828	+	0.966457i	$0.582677\pi$
$644$	117.012	−	9.72288i	0.181696	−	0.0150976i
$645$	13.1428			0.0203765
$646$	1071.03	−	314.481i	1.65793	−	0.486813i
$647$	35.3165	+	40.7575i	0.0545851	+	0.0629945i	0.782385	−	0.622794i	$-0.214003\pi$
$647$	35.3165	+	40.7575i	0.0545851	+	0.0629945i	−0.727800	+	0.685789i	$0.759457\pi$
$648$	433.906	−	278.855i	0.669609	−	0.430331i
$649$	52.3189	−	7.52233i	0.0806147	−	0.0115906i
$650$	−57.1329	−	36.7171i	−0.0878968	−	0.0564879i
$651$	95.4374	+	43.5848i	0.146601	+	0.0669505i
$652$	51.9602	−	59.9652i	0.0796935	−	0.0919712i
$653$	48.4269	−	336.816i	0.0741606	−	0.515798i	−0.918553	−	0.395298i	$-0.870641\pi$
$653$	48.4269	−	336.816i	0.0741606	−	0.515798i	0.992713	−	0.120500i	$-0.0384497\pi$
$654$	185.752	−	84.8299i	0.284024	−	0.129709i
$655$	−79.4894	+	270.716i	−0.121358	+	0.413307i
$656$	142.375	+	41.8051i	0.217035	+	0.0637273i
$657$	−326.118	−	714.099i	−0.496374	−	1.08691i
$658$	256.339	+	36.8559i	0.389572	+	0.0560120i
$659$	−571.880	−	495.537i	−0.867800	−	0.751953i	0.102276	−	0.994756i	$-0.467388\pi$
$659$	−571.880	−	495.537i	−0.867800	−	0.751953i	−0.970076	+	0.242803i	$0.921933\pi$
$660$	−1.33983	+	2.93381i	−0.00203004	+	0.00444517i
$661$	−237.960	+	370.273i	−0.360000	+	0.560171i	−0.973259	−	0.229711i	$-0.926222\pi$
$661$	−237.960	+	370.273i	−0.360000	+	0.560171i	0.613259	+	0.789882i	$0.289858\pi$
$662$	25.1514	+	174.932i	0.0379930	+	0.264247i
$663$	−23.9135	−	37.2102i	−0.0360687	−	0.0561239i
$664$	−394.111	+	341.499i	−0.593541	+	0.514306i
$665$	−46.6923	−	159.019i	−0.0702140	−	0.239127i
$666$		−	740.605i		−	1.11202i
$667$	297.434	+	217.364i	0.445929	+	0.325882i
$668$	113.609			0.170073
$669$	99.3825	−	29.1813i	0.148554	−	0.0436193i
$670$	141.559	+	163.368i	0.211282	+	0.243833i
$671$	54.7435	−	35.1815i	0.0815849	−	0.0524315i
$672$	−66.7601	+	9.59866i	−0.0993454	+	0.0142837i
$673$	154.231	+	99.1181i	0.229169	+	0.147278i	0.650187	−	0.759774i	$-0.274691\pi$
$673$	154.231	+	99.1181i	0.229169	+	0.147278i	−0.421018	+	0.907052i	$0.638327\pi$
$674$	625.500	+	285.656i	0.928042	+	0.423822i
$675$	220.797	−	254.813i	0.327107	−	0.377501i
$676$	−40.5070	+	281.732i	−0.0599216	+	0.416764i
$677$	−923.898	+	421.930i	−1.36469	+	0.623235i	−0.957055	−	0.289907i	$-0.906375\pi$
$677$	−923.898	+	421.930i	−1.36469	+	0.623235i	−0.407640	+	0.913143i	$0.633648\pi$
$678$	−20.1895	+	68.7591i	−0.0297780	+	0.101415i
$679$	−237.957	−	69.8706i	−0.350453	−	0.102902i
$680$	−152.877	−	334.754i	−0.224819	−	0.492285i
$681$	190.864	+	27.4421i	0.280270	+	0.0402968i
$682$	51.7619	+	44.8520i	0.0758973	+	0.0657654i
$683$	345.384	−	756.285i	0.505686	−	1.10730i	−0.468893	−	0.883255i	$-0.655347\pi$
$683$	345.384	−	756.285i	0.505686	−	1.10730i	0.974579	−	0.224043i	$-0.0719258\pi$
$684$	−238.816	+	371.605i	−0.349146	+	0.543282i
$685$	21.0937	+	146.710i	0.0307938	+	0.214176i
$686$	−214.925	−	334.429i	−0.313301	−	0.487506i
$687$	−160.834	+	139.363i	−0.234110	+	0.202858i
$688$	13.9555	+	47.5279i	0.0202841	+	0.0690813i
$689$		−	82.7526i		−	0.120105i
$690$	−49.5700	−	26.3317i	−0.0718405	−	0.0381618i
$691$	323.621			0.468337			0.234169	−	0.972196i	$-0.424763\pi$
$691$	323.621			0.468337			0.234169	+	0.972196i	$0.424763\pi$
$692$	−174.595	+	51.2656i	−0.252304	+	0.0740832i
$693$	−18.2624	−	21.0759i	−0.0263527	−	0.0304126i
$694$	−157.242	+	101.053i	−0.226573	+	0.145610i
$695$	371.520	−	53.4166i	0.534562	−	0.0768583i
$696$	−104.822	−	67.3650i	−0.150606	−	0.0967889i
$697$	−524.695	−	239.620i	−0.752791	−	0.343788i
$698$	38.2664	−	44.1618i	0.0548230	−	0.0632691i
$699$	−36.6142	+	254.658i	−0.0523809	+	0.364317i
$700$	101.099	−	46.1702i	0.144427	−	0.0659574i
$701$	105.542	−	359.441i	0.150559	−	0.512755i	−0.849327	−	0.527867i	$-0.822992\pi$
$701$	105.542	−	359.441i	0.150559	−	0.512755i	0.999886	+	0.0151114i	$0.00481028\pi$
$702$	−46.3537	−	13.6107i	−0.0660308	−	0.0193884i
$703$	778.222	+	1704.07i	1.10700	+	2.42399i
$704$	−71.4332	−	10.2706i	−0.101468	−	0.0145888i
$705$	71.1595	+	61.6600i	0.100935	+	0.0874610i
$706$	−232.984	+	510.164i	−0.330006	+	0.722612i
$707$	−166.170	+	258.566i	−0.235036	+	0.365723i
$708$	10.1593	+	70.6592i	0.0143492	+	0.0998011i
$709$	−380.584	−	592.201i	−0.536790	−	0.835262i	0.461873	−	0.886946i	$-0.347178\pi$
$709$	−380.584	−	592.201i	−0.536790	−	0.835262i	−0.998663	+	0.0516838i	$0.983541\pi$
$710$	125.554	−	108.793i	0.176836	−	0.153229i
$711$	−50.2676	−	171.196i	−0.0706999	−	0.240782i
$712$		−	604.758i		−	0.849380i
$713$	633.610	−	648.356i	0.888653	−	0.909335i
$714$	−95.1749			−0.133298
$715$	−4.11346	+	1.20782i	−0.00575309	+	0.00168926i
$716$	−297.121	−	342.896i	−0.414974	−	0.478905i
$717$	293.580	−	188.672i	0.409456	−	0.263142i
$718$	−330.584	+	47.5308i	−0.460423	+	0.0661988i
$719$	−156.106	−	100.324i	−0.217116	−	0.139532i	0.427562	−	0.903986i	$-0.359372\pi$
$719$	−156.106	−	100.324i	−0.217116	−	0.139532i	−0.644679	+	0.764454i	$0.723009\pi$
$720$	−81.6687	−	37.2969i	−0.113429	−	0.0518012i
$721$	−21.3049	+	24.5872i	−0.0295491	+	0.0341015i
$722$	−131.638	+	915.562i	−0.182324	+	1.26809i
$723$	−129.029	+	58.9258i	−0.178464	+	0.0815018i
$724$	−105.955	+	360.848i	−0.146346	+	0.498409i
$725$	334.586	+	98.2432i	0.461497	+	0.135508i
$726$	−67.5165	−	147.840i	−0.0929979	−	0.203637i
$727$	−1175.29	−	168.981i	−1.61663	−	0.232437i	−0.726177	−	0.687508i	$-0.758705\pi$
$727$	−1175.29	−	168.981i	−1.61663	−	0.232437i	−0.890455	+	0.455071i	$0.849614\pi$
$728$	−39.8948	−	34.5690i	−0.0548005	−	0.0474849i
$729$	−151.033	+	330.716i	−0.207179	+	0.453658i
$730$	−140.393	+	218.456i	−0.192319	+	0.299254i
$731$	−27.4035	−	190.596i	−0.0374877	−	0.260733i
$732$	47.5143	+	73.9337i	0.0649102	+	0.101002i
$733$	232.509	−	201.470i	0.317202	−	0.274857i	−0.481677	−	0.876349i	$-0.659972\pi$
$733$	232.509	−	201.470i	0.317202	−	0.274857i	0.798879	+	0.601492i	$0.205427\pi$
$734$	−65.7260	−	223.842i	−0.0895449	−	0.304962i
$735$		−	65.2023i		−	0.0887106i
$736$	−117.319	+	570.840i	−0.159400	+	0.775597i
$737$	−92.0077			−0.124841
$738$	−287.971	+	84.5558i	−0.390204	+	0.114574i
$739$	681.439	+	786.423i	0.922110	+	1.06417i	0.997751	+	0.0670365i	$0.0213544\pi$
$739$	681.439	+	786.423i	0.922110	+	1.06417i	−0.0756405	+	0.997135i	$0.524100\pi$
$740$	156.743	−	100.733i	0.211815	−	0.136126i
$741$	57.6223	−	8.28484i	0.0777629	−	0.0111806i
$742$	−149.795	−	96.2673i	−0.201880	−	0.129740i
$743$	−797.605	−	364.254i	−1.07349	−	0.490248i	−0.201360	−	0.979517i	$-0.564536\pi$
$743$	−797.605	−	364.254i	−1.07349	−	0.490248i	−0.872132	+	0.489270i	$0.837263\pi$
$744$	−200.795	+	231.729i	−0.269885	+	0.311464i
$745$	70.3405	−	489.229i	0.0944168	−	0.656683i
$746$	−366.160	+	167.220i	−0.490831	+	0.224155i
$747$	139.334	−	474.528i	0.186525	−	0.635245i
$748$	45.3394	+	13.3129i	0.0606142	+	0.0177979i
$749$	−86.8946	−	190.273i	−0.116014	−	0.254035i
$750$	−112.979	−	16.2440i	−0.150639	−	0.0216586i
$751$	−248.281	−	215.137i	−0.330601	−	0.286467i	0.473704	−	0.880684i	$-0.342917\pi$
$751$	−248.281	−	215.137i	−0.330601	−	0.286467i	−0.804305	+	0.594217i	$0.797462\pi$
$752$	−147.420	+	322.804i	−0.196037	+	0.429261i
$753$	−74.8087	+	116.405i	−0.0993475	+	0.154588i
$754$	−7.11072	−	49.4562i	−0.00943067	−	0.0655917i
$755$	131.023	+	203.875i	0.173540	+	0.270033i
$756$	59.7502	−	51.7739i	0.0790347	−	0.0684840i
$757$	31.4162	+	106.994i	0.0415009	+	0.141339i	0.977637	−	0.210298i	$-0.0674433\pi$
$757$	31.4162	+	106.994i	0.0415009	+	0.141339i	−0.936136	+	0.351637i	$0.885625\pi$
$758$		−	361.640i		−	0.477097i
$759$	22.2868	−	8.60583i	0.0293634	−	0.0113384i
$760$	484.350			0.637302
$761$	143.180	−	42.0416i	0.188148	−	0.0552452i	−0.186301	−	0.982493i	$-0.559650\pi$
$761$	143.180	−	42.0416i	0.188148	−	0.0552452i	0.374449	+	0.927247i	$0.377832\pi$
$762$	−104.416	−	120.503i	−0.137029	−	0.158140i
$763$	−373.690	+	240.156i	−0.489764	+	0.314752i
$764$	−588.449	+	84.6062i	−0.770222	+	0.110741i
$765$	293.607	+	188.690i	0.383800	+	0.246653i
$766$	573.345	+	261.838i	0.748492	+	0.341825i
$767$	−62.1383	+	71.7114i	−0.0810147	+	0.0934960i
$768$	33.4602	−	232.720i	0.0435679	−	0.303021i
$769$	−91.5230	+	41.7972i	−0.119016	+	0.0543526i	−0.474033	−	0.880507i	$-0.657202\pi$
$769$	−91.5230	+	41.7972i	−0.119016	+	0.0543526i	0.355017	+	0.934860i	$0.384475\pi$
$770$	−2.59890	+	8.85105i	−0.00337520	+	0.0114949i
$771$	−132.243	−	38.8301i	−0.171521	−	0.0503632i
$772$	76.2597	+	166.985i	0.0987820	+	0.216302i
$773$	1323.30	+	190.262i	1.71190	+	0.246135i	0.927422	−	0.374017i	$-0.122020\pi$
$773$	1323.30	+	190.262i	1.71190	+	0.246135i	0.784482	+	0.620152i	$0.212929\pi$
$774$	−75.7179	−	65.6099i	−0.0978268	−	0.0847674i
$775$	356.472	−	780.564i	0.459964	−	1.00718i
$776$	391.847	−	609.726i	0.504958	−	0.785729i
$777$	−22.7319	−	158.104i	−0.0292560	−	0.203480i
$778$	−13.4512	−	20.9305i	−0.0172895	−	0.0269030i
$779$	573.745	−	497.153i	0.736514	−	0.638193i
$780$	−1.63122	−	5.55542i	−0.00209130	−	0.00712233i
$781$			70.7108i			0.0905388i
$782$	−278.502	+	773.761i	−0.356141	+	0.989464i
$783$	248.055			0.316801
$784$	235.789	−	69.2338i	0.300751	−	0.0883085i
$785$	−201.796	−	232.885i	−0.257065	−	0.296668i
$786$	−179.396	+	115.291i	−0.228239	+	0.146680i
$787$	999.611	−	143.722i	1.27015	−	0.182621i	0.525917	−	0.850536i	$-0.323722\pi$
$787$	999.611	−	143.722i	1.27015	−	0.182621i	0.744237	+	0.667916i	$0.232813\pi$
$788$	209.623	+	134.717i	0.266020	+	0.170960i
$789$	−98.7687	−	45.1061i	−0.125182	−	0.0571688i
$790$	−38.6495	+	44.6040i	−0.0489235	+	0.0564607i
$791$	22.1849	−	154.299i	0.0280466	−	0.195068i
$792$	74.1353	−	33.8565i	0.0936052	−	0.0427481i
$793$	−32.9118	+	112.087i	−0.0415028	+	0.141346i
$794$	225.547	+	66.2266i	0.284064	+	0.0834088i
$795$	−26.8936	−	58.8889i	−0.0338285	−	0.0740740i
$796$	377.934	+	54.3387i	0.474792	+	0.0682647i
$797$	790.527	+	684.996i	0.991879	+	0.859468i	0.990076	−	0.140531i	$-0.0448808\pi$
$797$	790.527	+	684.996i	0.991879	+	0.859468i	0.00180236	+	0.999998i	$0.499426\pi$
$798$	52.0360	−	113.943i	0.0652080	−	0.142786i
$799$	745.815	−	1160.51i	0.933435	−	1.45245i
$800$	78.5056	+	546.019i	0.0981320	+	0.682523i
$801$	310.077	+	482.490i	0.387113	+	0.602359i
$802$	−551.407	+	477.797i	−0.687540	+	0.595757i
$803$	−31.1393	−	106.051i	−0.0387787	−	0.132068i
$804$		−	124.261i		−	0.154553i
$805$	114.883	+	41.3504i	0.142712	+	0.0513669i
$806$	−122.954			−0.152548
$807$	46.7788	−	13.7355i	0.0579663	−	0.0170204i
$808$	−588.225	−	678.848i	−0.728002	−	0.840159i
$809$	−132.837	+	85.3694i	−0.164199	+	0.105525i	−0.620160	−	0.784476i	$-0.712932\pi$
$809$	−132.837	+	85.3694i	−0.164199	+	0.105525i	0.455960	+	0.890000i	$0.349296\pi$
$810$	160.158	−	23.0273i	0.197726	−	0.0284287i
$811$	−685.940	−	440.827i	−0.845795	−	0.543559i	0.0444657	−	0.999011i	$-0.485841\pi$
$811$	−685.940	−	440.827i	−0.845795	−	0.543559i	−0.890261	+	0.455452i	$0.849478\pi$
$812$	74.3787	+	33.9676i	0.0915994	+	0.0418321i
$813$	−124.944	+	144.193i	−0.153682	+	0.177359i
$814$	14.8394	−	103.210i	0.0182302	−	0.126794i
$815$	75.0536	−	34.2758i	0.0920903	−	0.0420562i
$816$	36.7431	−	125.135i	0.0450283	−	0.153352i
$817$	243.163	+	71.3990i	0.297629	+	0.0873917i
$818$	−55.1800	−	120.827i	−0.0674572	−	0.147711i
$819$	49.5535	+	7.12471i	0.0605049	+	0.00869929i
$820$	−57.0637	−	49.4460i	−0.0695899	−	0.0603000i
$821$	−432.473	+	946.983i	−0.526764	+	1.15345i	0.440051	+	0.897973i	$0.354960\pi$
$821$	−432.473	+	946.983i	−0.526764	+	1.15345i	−0.966815	+	0.255479i	$0.917767\pi$
$822$	−60.5655	+	94.2418i	−0.0736807	+	0.114649i
$823$	−55.7113	−	387.481i	−0.0676930	−	0.470815i	−0.995267	−	0.0971761i	$-0.969019\pi$
$823$	−55.7113	−	387.481i	−0.0676930	−	0.470815i	0.927574	−	0.373639i	$-0.121890\pi$
$824$	−51.4032	−	79.9849i	−0.0623825	−	0.0970691i
$825$	17.0906	−	14.8091i	0.0207159	−	0.0179504i
$826$	57.5222	+	195.903i	0.0696394	+	0.237170i
$827$			621.963i			0.752071i	0.926605	+	0.376036i	$0.122713\pi$
$827$			621.963i			0.752071i	−0.926605	+	0.376036i	$0.877287\pi$
$828$	−117.225	−	303.582i	−0.141576	−	0.366645i
$829$	−593.876			−0.716377			−0.358188	−	0.933649i	$-0.616605\pi$
$829$	−593.876			−0.716377			−0.358188	+	0.933649i	$0.616605\pi$
$830$	−156.966	+	46.0894i	−0.189116	+	0.0555294i
$831$	101.241	+	116.839i	0.121831	+	0.140600i
$832$	108.988	−	70.0423i	0.130995	−	0.0841855i
$833$	−945.556	+	135.950i	−1.13512	+	0.163206i
$834$	238.652	+	153.373i	0.286154	+	0.183900i
$835$	107.464	+	49.0769i	0.128699	+	0.0587748i
$836$	−40.7270	+	47.0014i	−0.0487165	+	0.0562218i
$837$	86.8712	−	604.202i	0.103789	−	0.721867i
$838$	505.123	−	230.682i	0.602772	−	0.275277i
$839$	−223.108	+	759.837i	−0.265922	+	0.905646i	0.712958	+	0.701207i	$0.247355\pi$
$839$	−223.108	+	759.837i	−0.265922	+	0.905646i	−0.978879	+	0.204439i	$0.934463\pi$
$840$	−39.6246	−	11.6348i	−0.0471722	−	0.0138510i
$841$	−242.790	−	531.636i	−0.288692	−	0.632147i
$842$	94.9910	+	13.6576i	0.112816	+	0.0162205i
$843$	−125.178	−	108.467i	−0.148491	−	0.128668i
$844$	19.3071	−	42.2766i	0.0228757	−	0.0500908i
$845$	−160.019	+	248.995i	−0.189372	+	0.294669i
$846$	−102.150	−	710.467i	−0.120744	−	0.839795i
$847$	191.141	+	297.422i	0.225669	+	0.351147i
$848$	184.401	−	159.785i	0.217454	−	0.188425i
$849$	83.7891	+	285.359i	0.0986915	+	0.336112i
$850$			778.418i			0.915786i
$851$	−1351.88	−	277.839i	−1.58858	−	0.326485i
$852$	−95.4983			−0.112087
$853$	−1480.82	+	434.807i	−1.73601	+	0.509739i	−0.988067	−	0.154024i	$-0.950777\pi$
$853$	−1480.82	+	434.807i	−1.73601	+	0.509739i	−0.747943	+	0.663763i	$0.768959\pi$
$854$	164.608	+	189.968i	0.192749	+	0.222445i
$855$	−386.425	+	248.340i	−0.451959	+	0.290456i
$856$	605.087	−	86.9984i	0.706877	−	0.101634i
$857$	−621.593	−	399.473i	−0.725312	−	0.466130i	0.125169	−	0.992135i	$-0.460053\pi$
$857$	−621.593	−	399.473i	−0.725312	−	0.466130i	−0.850481	+	0.526006i	$0.823689\pi$
$858$	−2.94743	−	1.34605i	−0.00343524	−	0.00156882i
$859$	−540.926	+	624.262i	−0.629716	+	0.726731i	−0.977522	−	0.210836i	$-0.932382\pi$
$859$	−540.926	+	624.262i	−0.629716	+	0.726731i	0.347805	+	0.937567i	$0.386927\pi$
$860$	3.58712	−	24.9490i	0.00417108	−	0.0290105i
$861$	−58.8804	+	26.8898i	−0.0683861	+	0.0312309i
$862$	303.223	−	1032.68i	0.351767	−	1.19801i
$863$	−538.577	−	158.140i	−0.624075	−	0.183245i	−0.0456194	−	0.998959i	$-0.514526\pi$
$863$	−538.577	−	158.140i	−0.624075	−	0.183245i	−0.578455	+	0.815714i	$0.696344\pi$
$864$	163.010	+	356.943i	0.188669	+	0.413128i
$865$	−187.297	−	26.9292i	−0.216528	−	0.0311320i
$866$	735.077	+	636.948i	0.848818	+	0.735505i
$867$	−102.434	+	224.299i	−0.118147	+	0.258707i
$868$	108.785	−	169.273i	0.125328	−	0.195015i
$869$	−3.57504	−	24.8649i	−0.00411397	−	0.0286133i
$870$	−21.1328	−	32.8833i	−0.0242906	−	0.0377969i
$871$	124.828	−	108.164i	0.143315	−	0.124183i
$872$	−365.740	−	1245.60i	−0.419426	−	1.42844i
$873$			687.364i			0.787359i
$874$	−774.074	−	756.468i	−0.885668	−	0.865524i
$875$	248.291			0.283761
$876$	143.226	−	42.0551i	0.163500	−	0.0480081i
$877$	6.21935	+	7.17752i	0.00709162	+	0.00818417i	0.759284	−	0.650759i	$-0.225549\pi$
$877$	6.21935	+	7.17752i	0.00709162	+	0.00818417i	−0.752193	+	0.658943i	$0.771004\pi$
$878$	53.8561	−	34.6112i	0.0613395	−	0.0394205i
$879$	−36.8972	+	5.30502i	−0.0419763	+	0.00603528i
$880$	−10.6340	−	6.83405i	−0.0120841	−	0.00776596i
$881$	461.029	+	210.545i	0.523302	+	0.238984i	0.659510	−	0.751696i	$-0.270764\pi$
$881$	461.029	+	210.545i	0.523302	+	0.238984i	−0.136207	+	0.990680i	$0.543491\pi$
$882$	−325.495	+	375.641i	−0.369042	+	0.425897i
$883$	132.555	−	921.938i	0.150119	−	1.04410i	−0.765900	−	0.642960i	$-0.777706\pi$
$883$	132.555	−	921.938i	0.150119	−	1.04410i	0.916018	−	0.401137i	$-0.131385\pi$
$884$	−77.1628	+	35.2391i	−0.0872883	+	0.0398632i
$885$	−20.9138	+	71.2259i	−0.0236314	+	0.0804812i
$886$	−955.233	−	280.482i	−1.07814	−	0.316571i
$887$	306.514	+	671.171i	0.345562	+	0.756676i	1.00000		0.000559720i	$0.000178164\pi$
$887$	306.514	+	671.171i	0.345562	+	0.756676i	−0.654438	+	0.756116i	$0.727095\pi$
$888$	462.055	+	66.4334i	0.520332	+	0.0748124i
$889$	262.129	+	227.136i	0.294858	+	0.255496i
$890$	78.8111	−	172.572i	0.0885518	−	0.193901i
$891$	−37.2337	+	57.9368i	−0.0417887	+	0.0650244i
$892$	−28.2700	−	196.622i	−0.0316928	−	0.220429i
$893$	981.590	+	1527.38i	1.09921	+	1.71040i
$894$	282.323	−	244.634i	0.315798	−	0.273640i
$895$	−132.925	−	452.700i	−0.148519	−	0.505810i
$896$			20.6580i			0.0230558i
$897$	−20.1197	+	37.8758i	−0.0224300	+	0.0422250i
$898$	1114.81			1.24144
$899$	605.743	−	177.862i	0.673797	−	0.197845i
$900$	−201.724	−	232.802i	−0.224138	−	0.258669i
$901$	−797.925	+	512.795i	−0.885599	+	0.569140i
$902$	−41.8256	+	6.01361i	−0.0463698	+	0.00666698i
$903$	−18.1780	−	11.6823i	−0.0201307	−	0.0129372i
$904$	414.403	+	189.251i	0.458410	+	0.209349i
$905$	−256.104	+	295.560i	−0.282988	+	0.326585i
$906$	−26.0676	+	181.304i	−0.0287722	+	0.200115i
$907$	638.704	−	291.687i	0.704195	−	0.321595i	−0.0309351	−	0.999521i	$-0.509849\pi$
$907$	638.704	−	291.687i	0.704195	−	0.321595i	0.735130	+	0.677927i	$0.237121\pi$
$908$	104.187	−	354.827i	0.114743	−	0.390779i
$909$	817.365	+	240.000i	0.899191	+	0.264026i
$910$	−6.87929	−	15.0635i	−0.00755966	−	0.0165533i
$911$	330.827	+	47.5657i	0.363147	+	0.0522127i	0.321473	−	0.946919i	$-0.395822\pi$
$911$	330.827	+	47.5657i	0.363147	+	0.0522127i	0.0416737	+	0.999131i	$0.486731\pi$
$912$	129.723	+	112.405i	0.142240	+	0.123251i
$913$	28.9255	−	63.3381i	0.0316818	−	0.0693736i
$914$	350.151	−	544.846i	0.383098	−	0.596112i
$915$	13.0062	+	90.4600i	0.0142144	+	0.0988633i
$916$	220.656	+	343.347i	0.240891	+	0.374833i
$917$	350.575	−	303.775i	0.382307	−	0.331271i
$918$	156.003	+	531.297i	0.169938	+	0.578754i
$919$		−	914.303i		−	0.994889i	−0.867496	−	0.497444i	$-0.834272\pi$
$919$		−	914.303i		−	0.994889i	0.867496	−	0.497444i	$-0.165728\pi$
$920$	−210.540	+	288.097i	−0.228848	+	0.313149i
$921$	129.553			0.140665
$922$	10.4909	−	3.08042i	0.0113785	−	0.00334102i
$923$	−83.1272	−	95.9339i	−0.0900620	−	0.103937i
$924$	4.46092	−	2.86686i	0.00482784	−	0.00310266i
$925$	−1293.10	+	185.920i	−1.39795	+	0.200995i
$926$	291.033	+	187.035i	0.314290	+	0.201982i
$927$	82.0212	+	37.4578i	0.0884803	+	0.0404076i
$928$	−265.768	+	306.713i	−0.286388	+	0.330510i
$929$	162.255	−	1128.51i	0.174655	−	1.21475i	−0.694235	−	0.719749i	$-0.744257\pi$
$929$	162.255	−	1128.51i	0.174655	−	1.21475i	0.868890	−	0.495005i	$-0.164834\pi$
$930$	−87.4968	+	39.9585i	−0.0940826	+	0.0429661i
$931$	354.215	−	1206.34i	0.380467	−	1.29575i
$932$	473.423	+	139.010i	0.507965	+	0.149152i
$933$	202.002	+	442.324i	0.216509	+	0.474088i
$934$	889.043	+	127.825i	0.951867	+	0.136858i
$935$	37.1361	+	32.1786i	0.0397177	+	0.0344156i
$936$	−60.7785	+	133.086i	−0.0649343	+	0.142186i
$937$	886.734	−	1379.79i	0.946355	−	1.47256i	0.0662353	−	0.997804i	$-0.478901\pi$
$937$	886.734	−	1379.79i	0.946355	−	1.47256i	0.880119	−	0.474753i	$-0.157462\pi$
$938$	−50.5790	−	351.785i	−0.0539222	−	0.375037i
$939$	−252.319	−	392.616i	−0.268710	−	0.418122i
$940$	136.471	−	118.253i	0.145182	−	0.125801i
$941$	376.647	+	1282.74i	0.400263	+	1.36317i	0.875460	+	0.483291i	$0.160559\pi$
$941$	376.647	+	1282.74i	0.400263	+	1.36317i	−0.475197	+	0.879880i	$0.657623\pi$
$942$		−	232.904i		−	0.247244i
$943$	46.3139	+	557.376i	0.0491133	+	0.591067i
$944$	−279.779			−0.296376
$945$	78.8837	−	23.1624i	0.0834749	−	0.0245104i
$946$	−9.23738	−	10.6605i	−0.00976467	−	0.0112690i
$947$	−311.098	+	199.931i	−0.328509	+	0.211120i	−0.694490	−	0.719502i	$-0.744370\pi$
$947$	−311.098	+	199.931i	−0.328509	+	0.211120i	0.365981	+	0.930622i	$0.380734\pi$
$948$	33.5813	−	4.82826i	0.0354233	−	0.00509310i
$949$	166.919	+	107.273i	0.175890	+	0.113037i
$950$	−931.918	−	425.593i	−0.980966	−	0.447992i
$951$	−238.101	+	274.783i	−0.250369	+	0.288941i
$952$	−86.1076	+	598.891i	−0.0904491	+	0.629087i
$953$	−981.065	+	448.037i	−1.02945	+	0.470134i	−0.857235	−	0.514926i	$-0.827819\pi$
$953$	−981.065	+	448.037i	−1.02945	+	0.470134i	−0.172214	+	0.985060i	$0.555092\pi$
$954$	−139.039	+	473.523i	−0.145743	+	0.496356i
$955$	−593.168	−	174.170i	−0.621119	−	0.182377i
$956$	−278.029	−	608.798i	−0.290825	−	0.636818i
$957$	16.4680	+	2.36774i	0.0172079	+	0.00247413i
$958$	−254.537	−	220.557i	−0.265696	−	0.230227i
$959$	101.232	−	221.667i	0.105560	−	0.231144i
$960$	54.7957	−	85.2637i	0.0570788	−	0.0888164i
$961$	−84.3282	−	586.516i	−0.0877505	−	0.610318i
$962$	101.201	+	157.471i	0.105198	+	0.163691i
$963$	−438.145	+	379.655i	−0.454980	+	0.394242i
$964$	76.6422	+	261.019i	0.0795044	+	0.270767i
$965$			190.896i			0.197820i
$966$	45.1554	+	80.4811i	0.0467447	+	0.0833138i
$967$	1192.67			1.23337			0.616687	−	0.787209i	$-0.288475\pi$
$967$	1192.67			1.23337			0.616687	+	0.787209i	$0.288475\pi$
$968$	−991.375	+	291.094i	−1.02415	+	0.300717i
$969$	−436.954	−	504.272i	−0.450933	−	0.520404i
$970$	191.275	−	122.925i	0.197191	−	0.126727i
$971$	779.548	−	112.082i	0.802830	−	0.115429i	0.271328	−	0.962487i	$-0.412537\pi$
$971$	779.548	−	112.082i	0.802830	−	0.115429i	0.531501	+	0.847057i	$0.321628\pi$
$972$	−280.863	−	180.499i	−0.288953	−	0.185699i
$973$	−561.336	−	256.353i	−0.576912	−	0.263467i
$974$	−526.101	+	607.153i	−0.540145	+	0.623361i
$975$	−5.77748	+	40.1833i	−0.00592562	+	0.0412136i
$976$	−313.317	+	143.087i	−0.321021	+	0.146606i
$977$	316.018	−	1076.26i	0.323457	−	1.10159i	−0.623923	−	0.781486i	$-0.714462\pi$
$977$	316.018	−	1076.26i	0.323457	−	1.10159i	0.947381	−	0.320109i	$-0.103720\pi$
$978$	59.8357	+	17.5694i	0.0611817	+	0.0179646i
$979$	33.5446	+	73.4524i	0.0342641	+	0.0750279i
$980$	−123.773	−	17.7959i	−0.126299	−	0.0181591i
$981$	930.449	+	806.238i	0.948469	+	0.821853i
$982$	−83.4798	+	182.795i	−0.0850099	+	0.186146i
$983$	238.414	−	370.979i	0.242537	−	0.377394i	−0.698549	−	0.715562i	$-0.746171\pi$
$983$	238.414	−	370.979i	0.242537	−	0.377394i	0.941086	+	0.338168i	$0.109807\pi$
$984$	−26.9219	−	187.246i	−0.0273597	−	0.190291i
$985$	140.090	+	217.984i	0.142223	+	0.221303i
$986$	−432.807	+	375.030i	−0.438952	+	0.380354i
$987$	−43.6137	−	148.535i	−0.0441881	−	0.150491i
$988$		−	111.646i		−	0.113002i
$989$	−148.169	+	113.600i	−0.149817	+	0.114864i
$990$	25.5672			0.0258254
$991$	−835.248	+	245.251i	−0.842834	+	0.247478i	−0.674521	−	0.738255i	$-0.735650\pi$
$991$	−835.248	+	245.251i	−0.842834	+	0.247478i	−0.168312	+	0.985734i	$0.553832\pi$
$992$	654.005	+	754.762i	0.659279	+	0.760848i
$993$	88.8725	−	57.1149i	0.0894990	−	0.0575175i
$994$	−270.358	+	38.8716i	−0.271990	+	0.0391062i
$995$	334.018	+	214.660i	0.335697	+	0.215739i
$996$	85.5411	+	39.0653i	0.0858846	+	0.0392222i
$997$	−278.931	+	321.903i	−0.279770	+	0.322872i	−0.878191	−	0.478310i	$-0.841250\pi$
$997$	−278.931	+	321.903i	−0.279770	+	0.322872i	0.598421	+	0.801182i	$0.295795\pi$
$998$	145.648	−	1013.00i	0.145940	−	1.01503i
$999$	−845.326	+	386.047i	−0.846172	+	0.386434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.14.3	yes	30
3.2	odd	2		207.3.j.a.37.1		30
4.3	odd	2		368.3.p.a.129.2		30
23.5	odd	22	inner	23.3.d.a.5.3	✓	30
23.8	even	11		529.3.b.b.528.9		30
23.15	odd	22		529.3.b.b.528.10		30
69.5	even	22		207.3.j.a.28.1		30
92.51	even	22		368.3.p.a.97.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.5.3	✓	30	23.5	odd	22	inner
23.3.d.a.14.3	yes	30	1.1	even	1	trivial
207.3.j.a.28.1		30	69.5	even	22
207.3.j.a.37.1		30	3.2	odd	2
368.3.p.a.97.2		30	92.51	even	22
368.3.p.a.129.2		30	4.3	odd	2
529.3.b.b.528.9		30	23.8	even	11
529.3.b.b.528.10		30	23.15	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44626 - 0.424661i) q^{2} +(-0.590042 - 0.680945i) q^{3} +(-1.45368 + 0.934223i) q^{4} +(-1.77862 + 0.255727i) q^{5} +(-1.14252 - 0.734256i) q^{6} +(2.68734 + 1.22727i) q^{7} +(-5.65401 + 6.52507i) q^{8} +(1.16530 - 8.10482i) q^{9} +O(q^{10})\)	\(q+(1.44626 - 0.424661i) q^{2} +(-0.590042 - 0.680945i) q^{3} +(-1.45368 + 0.934223i) q^{4} +(-1.77862 + 0.255727i) q^{5} +(-1.14252 - 0.734256i) q^{6} +(2.68734 + 1.22727i) q^{7} +(-5.65401 + 6.52507i) q^{8} +(1.16530 - 8.10482i) q^{9} +(-2.46375 + 1.12516i) q^{10} +(0.324790 - 1.10613i) q^{11} +(1.49389 + 0.438644i) q^{12} +(0.859718 + 1.88252i) q^{13} +(4.40777 + 0.633741i) q^{14} +(1.22359 + 1.06025i) q^{15} +(-2.53490 + 5.55065i) q^{16} +(12.8244 - 19.9551i) q^{17} +(-1.75647 - 12.2165i) q^{18} +(16.8785 + 26.2635i) q^{19} +(2.34663 - 2.03337i) q^{20} +(-0.749942 - 2.55407i) q^{21} -1.73768i q^{22} +(-22.9588 - 1.37682i) q^{23} +7.77931 q^{24} +(-20.8892 + 6.13363i) q^{25} +(2.04281 + 2.35753i) q^{26} +(-13.0284 + 8.37283i) q^{27} +(-5.05307 + 0.726522i) q^{28} +(-13.4745 - 8.65951i) q^{29} +(2.21988 + 1.01379i) q^{30} +(-25.8114 + 29.7879i) q^{31} +(3.60595 - 25.0799i) q^{32} +(-0.944855 + 0.431501i) q^{33} +(10.0732 - 34.3063i) q^{34} +(-5.09359 - 1.49561i) q^{35} +(5.87774 + 12.8705i) q^{36} +(59.3953 + 8.53975i) q^{37} +(35.5639 + 30.8163i) q^{38} +(0.774622 - 1.69619i) q^{39} +(8.38768 - 13.0515i) q^{40} +(-3.46071 - 24.0697i) q^{41} +(-2.16922 - 3.37538i) q^{42} +(6.13489 - 5.31592i) q^{43} +(0.561234 + 1.91139i) q^{44} +14.7134i q^{45} +(-33.7890 + 7.75844i) q^{46} +58.1561 q^{47} +(5.27538 - 1.54899i) q^{48} +(-26.3726 - 30.4356i) q^{49} +(-27.6066 + 17.7417i) q^{50} +(-21.1552 + 3.04166i) q^{51} +(-3.00845 - 1.93341i) q^{52} +(-36.3725 - 16.6108i) q^{53} +(-15.2868 + 17.6419i) q^{54} +(-0.294809 + 2.05044i) q^{55} +(-23.2022 + 10.5961i) q^{56} +(7.92496 - 26.9899i) q^{57} +(-23.1650 - 6.80184i) q^{58} +(19.0467 + 41.7064i) q^{59} +(-2.76922 - 0.398154i) q^{60} +(42.6597 + 36.9649i) q^{61} +(-24.6802 + 54.0422i) q^{62} +(13.0783 - 20.3503i) q^{63} +(-8.90898 - 61.9633i) q^{64} +(-2.01052 - 3.12843i) q^{65} +(-1.18327 + 1.02531i) q^{66} +(-22.4851 - 76.5774i) q^{67} +40.9891i q^{68} +(12.6091 + 16.4460i) q^{69} -8.00179 q^{70} +(-58.8521 + 17.2805i) q^{71} +(46.2959 + 53.4284i) q^{72} +(80.6553 - 51.8340i) q^{73} +(89.5276 - 12.8721i) q^{74} +(16.5022 + 10.6053i) q^{75} +(-49.0720 - 22.4104i) q^{76} +(2.23034 - 2.57395i) q^{77} +(0.400003 - 2.78208i) q^{78} +(19.8212 - 9.05205i) q^{79} +(3.08916 - 10.5207i) q^{80} +(-57.3197 - 16.8306i) q^{81} +(-15.2266 - 33.3415i) q^{82} +(59.7847 + 8.59575i) q^{83} +(3.47624 + 3.01218i) q^{84} +(-17.7066 + 38.7720i) q^{85} +(6.61520 - 10.2935i) q^{86} +(2.05385 + 14.2848i) q^{87} +(5.38123 + 8.37336i) q^{88} +(-52.9362 + 45.8694i) q^{89} +(6.24819 + 21.2794i) q^{90} +6.11407i q^{91} +(34.6609 - 19.4471i) q^{92} +35.5137 q^{93} +(84.1089 - 24.6966i) q^{94} +(-36.7367 - 42.3965i) q^{95} +(-19.2057 + 12.3428i) q^{96} +(-83.0916 + 11.9468i) q^{97} +(-51.0664 - 32.8184i) q^{98} +(-8.58653 - 3.92134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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